Geometric polarimetry − part I: spinors and wave states

A new formal approach for representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalised complex-analytic coherent wave as a generating line in the sphere of wave directions, and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincare sphere is now located in physical space, simply a coordination of the wave sphere, its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.

Global, local, or regional? The locus of MNE strategies

This paper provides an overview of the main insights arising from the ‘regional strategy’ literature. It also develops the contours of a new, rich research agenda for future international strategy scholarship, whereby the region should be introduced as an explicit, third geographic level of analysis, in addition to the country-level and the global level. Regional strategy analysis requires a fundamental rethink of mainstream theories in the international strategy sphere. This rethink involves, inter alia, internalization theory, with its resource-based view and transaction cost economics components, as well as the integration (I) – national responsiveness (NR) framework.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯Riemann zeta function in estimates for such GCD sums when 0<α<1/20<α<1/2.

The circulation of romances from England in late-medieval Ireland

The fifteenth century saw a striking upturn in the number of texts from foreign vernaculars that were translated into Irish. Indeed, one might go so far as to speak in terms of a ‘translation trend’ in Ireland during the mid to late fifteenth century. A notable feature of this trend is that a particularly high number of these Irish translations are of romances; contextual and textual evidence suggests that the original exemplars for many of these translated texts appear to have come from England, though not all of them were necessarily in English. Irish translations of eight romances have survived to the present day: Guy of Warwick; Bevis of Hampton; La Queste de Saint Graal; Fierabras; Caxton’s Recuyell of the Histories of Troie; William of Palerne; the Seven Sages of Rome; and Octavian. This paper addresses two aspects of these texts of particular relevance to romance scholars who do not work within the sphere of Celtic studies. Firstly, it argues that certain aspects of the dissemination and reception of romance in Ireland are quite distinctive. Manuscript and textual evidence suggests that the religious orders, particularly the Franciscans, seem to have played a role in the importation and translation of these narratives. Secondly, examination of the Irish versions of romance tends to bear out an observation made by Flower many years ago, but not pursued by subsequent scholars: ‘texts of an unusual kind were current in Ireland, and it may be that interesting discoveries are to be made here’. Certain narrative features of several of these Irish translations diverge from all the surviving versions of the relevant romance in other languages and may witness to a variant exemplar that has since been lost from its own linguistic corpus.