Compactification of the universal Picard over the moduli of stable curves

This article provides two different, but closely related, moduli problems, which in characteristic zero provide a type of compactification of the universal Picard over the moduli of stable curves. Although neither is of finite type, both are limits of a sequence of stacks, each of which is a separated algebraic stack of finite type. We discuss relations to previous compactifications and partial compactifications, give a number of examples related to this compactification, and work out the structure of its fibres over certain fixed curves. Some applications are also discussed. Received January 5, 1998; in final form April 1, 1999 / Published online July 3, 2000     

Zero and Infinite Curvature Limits of Hyperbolic Monopoles

We show that the zero curvature limit of the space of hyperbolicmonopoles gives the Euclidean monopoles, settling a conjectureof Atiyah. We also study the infinite curvature limit of thespace of hyperbolic monopoles, and show that the associatedrational maps appear explicitly here. 1991 Mathematics SubjectClassification 81T13, 53C07.     

Local internal supersymmetry of the free Maxwell theory

The free Maxwell theory is shown to possess an extended gauge invariance consisting of local internal supersymmetry transformations in addition to the usual local phase transformations. The Maxwell lagrangian is derived as a particular gauge choice in the extended theory.     

A Distribution Relation on Elliptic Curves

In this paper, we give an elementary proof of a curious identityof elliptic functions. It is very similar to a beautiful proofgiven by Coates of a different identity. The result was stronglymotivated by Wildeshaus' generalisation of Zagier's conjecture.1991 Mathematics Subject Classification 11G16, 33E05.     

Characterisation and identification of bacteria using SERS

Within microbiology Raman spectroscopy is considered as a very important whole-organism fingerprinting technique, which is used to characterise, discriminate and identify microorganisms and assess how they respond to abiotic or biotic stress. Enhancing the sensitivity of Raman spectroscopy is very beneficial for the rapid analysis of bacteria (and indeed biological systems in general), where the ultimate goal is to achieve this without the need for lengthy cell culture. Bypassing this step would provide significant benefits in many areas such as medical, environmental and industrial microbiology, microbial systems biology, biological warfare countermeasures and bioprocess monitoring. In this tutorial review we will report on the advances made in bacterial studies, a relatively new and exciting application area for SERS.     

A Remarkable cis‐ and trans‐Spanning Dibenzylidene Acetone Diphosphine Chelating Ligand (dbaphos)

A multidentate and flexible diolefin–diphosphine ligand, based on the dibenzylidene acetone core, namely dbaphos ( 1 ), is reported herein. The ligand adopts an array of different geometries at Pt, Pd and Rh. At Pt^II the dbaphos ligand forms cis‐ and trans‐diphosphine complexes and can be defined as a wide‐angle spanning ligand. ¹H NMR spectroscopic analysis shows that the β‐hydrogen of one olefin moiety interacts with the Pt^II centre (an anagostic interaction), which is supported by DFT calculations. At Pd⁰ and Rh^I, the dbaphos ligand exhibits both olefin and phosphine interactions with the metal centres. The Pd⁰ complex of dbaphos is dinuclear, with bridging diphosphines. The complex exhibits the coordination of one olefin moiety, which is in dynamic exchange (intramolecular) with the other “free” olefin. The Pd⁰ complex of dbaphos reacts with iodobenzene to afford trans‐[Pd^II(dbaphos)I(Ph)]. In the case of Rh^I, dbaphos coordinates to form a structure in which the phosphine and olefin moieties occupy both axial and equatorial sites, which stands in contrast to a related bidentate olefin, phosphine ligand (“Lei” ligand), in which the olefins occupy the equatorial sites and phosphines the axial sites, exclusively.