Conjectures are made on the text of three passages in Tibullus, Books 1–2: 1.4.26 hastam … suam for crines … suos, 2.1.56 membra for bache, 2.4.60 aliis rebus for alias herbas.

This article presents a new conjecture on Herodotus 1.51.3.

The ‘consensus’ model of public reason, associated with John Rawls’s political liberalism, has been criticised for excluding certain reasons from receiving consideration where the justification of the constitutional essentials is concerned. One limitation of these criticisms is that they typically focus on the exclusion of reasons political liberals are committed to excluding, notably reasons based on religious and comprehensive views. I argue that public reason excludes some reasons, central to the interests of many oppressed groups, that public reason advocates will agree should not be excluded.

A disease transmission model of SEIR type with exponential demographic structure is formulated, with a natural death rate constant and an excess death rate constant for infective individuals. The latent period is assumed to be constant, and the force of the infection is assumed to be of the standard form, namely, proportional to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The infected individuals are assumed not to be able to give birth and when an individual is removed fromthe I-class, it recovers, acquiring permanent immunity with probability f (0 ≤ f ≤ 1) and dies from the disease with probability 1 − f. The global attractiveness of the disease-free equilibrium, existence of the endemic equilibrium as well as the permanence criteria are investigated. Further, it is shown that for the special case of the model with zero latent period, R0 > 1 leads to the global stability of the endemic equilibrium, which completely answers the conjecture proposed by Diekmann and Heesterbeek.

Le système AutoGraphiX (AGX1 et AGX2) permet,parmi d'autres fonctions, la génération automatique de conjectures enthéorie des graphes et, dans une version plus récente, la preuve automatique de conjectures simples. Afind'illustrer ces fonctions et le type de résultats obtenus, nous étudions systématiquement ici des conjecturesobtenues par ce système et de la forme $\underline{b}_{n} \, \le \, g\,\oplus \,i \, \le \, \overline{b}_{n}$ où g désigne la maille (ou longueur du plus petit cycle) du graphe G=(V, E), i un autre invariant choisi parmi le nombre de stabilité, le rayon, le diamètre, le degré minimum, moyen ou maximum, $\underline{b}_{n} $ et $ \overline{b}_{n} $ des fonctions de l'ordre n = |V| de G les meilleures possibles, enfin $ \oplus $ correspond à une des opérations +,-,×,/. 48 telles conjectures sont obtenues: les plus simples sont démontréesautomatiquement et les autres à la main. De plus 12 autres conjecturesouvertes et non encore étudiées sont soumises aux lecteurs.