John Tzetzes and the blemish examiners : a Byzantine teacher on schedography, everyday language and writerly disposition

The paper focuses on John Tzetzes (ca. 1110-after 1166), a well-known teacher and scholar of the Komnenian era, with the aim of examining two issues. On the one hand, Tzetzes’ opinions about the teaching practice of schedography are collected and analysed, while, on the other, his opinions about everyday language and its possible uses are scrutinised through a close reading of many different passages from his works. In particular, the long epilogue of his Theogony (with its three parts united for the first time on the printed page), written for the sebastokratorissa Eirene around the middle of the Twelfth Century, is discussed in detail as a unique source of debate on what is the appropriate way of addressing and writing for audiences of different social and educational status. The analysis and interpretation of the texts demonstrates that the “idiosyncratic” personality Tzetzes shows in his writings is not a purely personal matter, but is strongly related to the competitive environment of the capital and to Tzetzes’ “middle-class” position in the Constantinopolitan society. The paper also demonstrates that the boundaries of usage between “learned” and “colloquial” discourse are quite fluid and this fluidity can be used in certain contexts to the advantage of a teacher in promoting his status and financial success, or to his disadvantage if he has to defend his choices against a rival. The paper ends with a broader analysis of the term oijkonomiva used by Tzetzes in the Theogony epilogue and of the meaning of this term within the system of literary patronage under the Komnenoi

The gravitational chiral anomaly of spin-1/2 field in the presence of twisted boundary conditions for ordinary field theory

We calculate the chiral anomaly in the neighbourhood of the fixed point space M_h which is constructed by the group action of a discrete symmetry h on a compact manifold M. The Feynman diagrams approach for the corresponding supersymmetric quantum mechanical system with twisted boundary conditions is used. The result we derive in this way agrees with the generalization of the ordinary index theorem (the G-index theorem) on the spin complex.Comment: 8 page

Self-similar solutions of R\'enyi's entropy and the concavity of its entropy power

We study the class of self-similar probability density functions with finite mean and variance which maximize R\'{e}nyi's entropy. The investigation is restricted in the Schwartz space $S(\mathbb{R}^d)$ and in the space of $l$-differentiable compactly supported functions $C_c^l(\mathbb{R}^d)$. Interestingly the solutions of this optimization problem do not coincide with the solutions of the usual porous medium equation with a Dirac point source, as it occurs in the optimization of Shannon's entropy. We also study the concavity of the entropy power in $\mathbb{R}^d$ with respect to time using two different methods. The first one takes advantage of the solutions determined earlier while the second one is based on a setting that could be used for Riemannian manifolds.Comment: 18 pages, 2 figure