Singularities of Type-Q ABS Equations

The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.Comment: contribution to the SIDE-9 special issue of SIGM

Elliptic Solutions of ABS Lattice Equations

Elliptic N-soliton-type solutions, i.e. solutions emerging from the application of N consecutive B\"acklund transformations to an elliptic seed solution, are constructed for all equations in the ABS list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.Comment: 42 pages, 3 diagram

Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis

We give integrable quad equations which are multi-quadratic (degree-two) counterparts of the well-known multi-affine (degree-one) equations classified by Adler, Bobenko and Suris (ABS). These multi-quadratic equations define multi-valued evolution from initial data, but our construction is based on the hypothesis that discriminants of the defining polynomial factorise in a particular way that allows to reformulate the equation as a single-valued system. Such reformulation comes at the cost of introducing auxiliary (edge) variables and augmenting the initial data. Like the multi-affine equations listed by ABS, these new models are consistent in multidimensions. We clarify their relationship with the ABS list by obtaining Backlund transformations connecting all but the primary multi-quadratic model back to equations from the multi-affine class.Comment: 21 pages, 2 figures, 3 table

Theoretical Studies of Several Small-Ring Precursors to (+)-JQ1

We present the results of DFT(B3LYP) calculations on several precursors to (+)-JQ1 using an accurate basis set, including a report of conformational analysis, thermochemistry, optimized geometries and electrostatic potentials, and calculated IR and Raman spectra. Species include (I)1H-1,4-diazepin-2(3H)-imine, (II) 9H-[1,2,4]triazolo[4,3-a][1,4]diazepine, (III) 6H-thieno[3,2-f][1,2,4]triazolo[4,3a][1,4]diazepine, and (IV) 4-(4-chlorophenyl)-6H-thieno[3,2f][1,2,4]triazolo[4,3-a][1,4]diazepine. Studies are also reported on monobrominated (II)-(IV) substituted at the chiral center of the seven member ring, including a comparison of the energetics of equatorial versus axial bromination of the parent precursor. Implications with regard to the larger structure of (+)-JQ1 are discussed

The Contrasting Soundscapes of Hull and London in David Bowie’s Ziggy Stardust and the Spiders from Mars

In this article I apply the concept of the urban soundscape as developed by Long and Collins (2012) in an analysis of the impact musicians from Hull had on the evolution of David Bowie’s seminal 1972 work The Rise and Fall of Ziggy Stardust and the Spiders from Mars. I argue that the performance of Ziggy Stardust, both on record and on stage, is doubly coded in relation to place and space. The 'concept' of The Rise and Fall of Ziggy Stardust as a musical, a fictional story with songs performed on stage, and an accompanying album of recorded songs, initially appears to be heavily associated with London. The format of the concept – which the creator described as theatre, rather than a rock and roll show – is derived from Bowie’s experience growing up in London from the late 1940s to the early 1970s, a time of great change in the capital. I suggest that the Ziggy Stardust performance, and its significance, rests on the authenticity of the supporting musicians in the project, musicians from Hull, Yorkshire, with whom Bowie had been playing for more than two years before it was aired. I illustrate that Bowie and his support cast were subject to different cultural settings, and thus influenced by different soundscapes, and the relevant properties from each are compared here. I go on to provide some assessment of how the involvement of these Hull musicians in the Bowie project has impacted upon the city’s historical music culture, and on heritage issues and cultural production in that town. I conclude by noting that Hull has a thriving arts community and is UK Capital of Culture in 2017