The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory

Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.Comment: 30 pages, 8 figures, 6 table

Pion polarizabilities: No conflict between dispersion theory and ChPT

Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected to non-analytic structuresComment: 9 pages, 4 figures; Proceedings of 6th International Workshop on Chiral Dynamics, 6-10 July 2009, Bern, Switzerlan

Relations Without Polyadic Properties: Albert the Great On the Nature and Ontological Status of Relations

I think it would be fair to say that, until about 1900, philosophers were generally reluctant to admit the existence of what are nowadays called polyadic properties.1 It is important to recognize, however, that this reluctance on the part of pre-twentieth-century philosophers did not prevent them from theorizing about relations. On the contrary, philosophers from the ancient through the modern period have had much to say about both the nature and the ontological status of relations. In this paper I examine the views of one such philosopher, namely, Albert the Grea

Analogues of Lusztig's higher order relations for the q-Onsager algebra

Let $A,A^*$ be the generators of the $q-$Onsager algebra. Analogues of Lusztig's $r-th$ higher order relations are proposed. In a first part, based on the properties of tridiagonal pairs of $q-$Racah type which satisfy the defining relations of the $q-$Onsager algebra, higher order relations are derived for $r$ generic. The coefficients entering in the relations are determined from a two-variable polynomial generating function. In a second part, it is conjectured that $A,A^*$ satisfy the higher order relations previously obtained. The conjecture is proven for $r=2,3$. For $r$ generic, using an inductive argument recursive formulae for the coefficients are derived. The conjecture is checked for several values of $r\geq 4$. Consequences for coideal subalgebras and integrable systems with boundaries at $q$ a root of unity are pointed out.Comment: 19 pages. v2: Some basic material in subsections 2.1,2.2,2.3 of pages 3-4 (Definitions 2.1,2.2, Lemma 2.2, Theorem 1) from Terwilliger's and coauthors works (see also arXiv:1307.7410); Missprints corrected; Minor changes in the text; References adde

Convex Relaxation of Optimal Power Flow, Part II: Exactness

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, June 2014. This is an extended version with Appendex VI that proves the main results in this tutoria

Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property

We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate ageing. A specific feature of such an approach dwells on the concept of semi-copula and in the extension, from copulas to semi-copulas, of properties of stochastic dependence. In this perspective, we aim to discuss some intricate aspects of conceptual character and to provide the readers with pertinent remarks from a Bayesian Statistics standpoint. In particular we will discuss the role of extensions of dependence properties. "Archimedean" models have an important role in the present framework. In the second part of the paper, the definitions of Kendall distribution and of Kendall equivalence classes will be extended to semi-copulas and related properties will be analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean" models and extend to them the analysis of the relations between the ageing notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD

Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, 15(1):15-27, March 2014. This is an extended version with Appendices VIII and IX that provide some mathematical preliminaries and proofs of the main result