What About the Bookstore?

There is often an assumption that academic libraries and bookstores are adversaries around the development of textbook affordability projects. This article shares the results of a survey on library-bookstore relationships and suggests that the two organizations have a shared interest in student success upon which a productive relationship can be built

Complexity in complex analysis

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.Comment: 30 pages, to appear in Advances in Mat

The Green's function and the Ahlfors map

The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analogue of the Riemann map in the multiply connected setting.Comment: 14 page

The structure of the semigroup of proper holomorphic mappings of a planar domain to the unit disc

Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that is an n-to-one branched covering with the properties that it extends continuously to the boundary and maps each boundary curve one-to-one onto the unit circle, and it maps each given point on the boundary to the point 1 in the unit circle. We modify a proof by H. Grunsky of Bieberbach's result to show that there is a rational function of 2n+2 complex variables that generates all of these maps. We also show how to generate all the proper holomorphic mappings to the unit disc via the rational function.Comment: 17 page

Functionalised nanostructured polyaniline? A new substrate for building adaptive sensing surfaces

A new method for covalently binding side-chains to the surface of solution based conducting polymer nanostructures is introduced in this paper. Modification of the structures is achieved by convenient reflux in the presence of a nucleophile, and post-functionalization purification is subsequently carried out by centrifugation. The entire process is easily scalable and hence suitable for bulk production of functionalized nanomaterials. In particular we focus on the modification of polyaniline nanofibres which can be synthesized by interfacial polymerization. Mercaptoundecanoic acid side-chains are attached to the polymer nanostructures, with the intrinsic nano-morphology of the material being maintained during the process. The modified PAni nanofibres provide a template for the attachment of other specific functional groups which could be used to target a particular species