Universal KZB equations I: the elliptic case

We define a universal version of the Knizhnik-Zamolodchikov-Bernard (KZB) connection in genus 1. This is a flat connection over a principal bundle on the moduli space of elliptic curves with marked points. It restricts to a flat connection on configuration spaces of points on elliptic curves, which can be used for proving the formality of the pure braid groups on genus 1 surfaces. We study the monodromy of this connection and show that it gives rise to a relation between the KZ associator and a generating series for iterated integrals of Eisenstein forms. We show that the universal KZB connection realizes as the usual KZB connection for simple Lie algebras, and that in the sl_n case this realization factors through the Cherednik algebras. This leads us to define a functor from the category of equivariant D-modules on sl_n to that of modules over the Cherednik algebra, and to compute the character of irreducible equivariant D-modules over sl_n which are supported on the nilpotent cone.Comment: Correction of reference of Thm. 9.12 stating an equivalence of categories between modules over the rational Cherednik algebra and its spherical subalgebr

Weight function for the quantum affine algebra Uq(sl^3)U_q(\hat{sl}_3)

We give a precise expression for the universal weight function of the quantum affine algebra $U_q(\hat{sl}_3)$. The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.Comment: 28 page

Nano-Engineering of Molecular Films by Self-Assembly and Langmuir-Blodgett Techniques

The availability of sophisticated and ultra-sensitive analytical tools and the maturity of organic synthesis have opened new possibilities for fabrication of molecular materials designed at the nanometer scale. Presently, the most promising and widely investigated methodologies are the self-assembly and Langmuir-Blodgett procedures. The former relies on the strong, preferential affinity of specific functional groups to solid surfaces, whereas the latter involves transfer of pre-formed mono layers at the air-water interface onto solid substrates. These techniques and their recent applications are reviewed

Nano-chemistry

Nanotechnology is a highly interdisciplinary field, with contributions from all fields: physics, chemistry, biology, materials science, engineering, and others. The explosive number of publications in this field makes it nearly impossible to give an extensive review even in chemistry alone. Nonetheless, one may track its emergence and rapid advancement from the point of view of a chemist\u27s. This paper aims to provide a conceptual overview of chemistry for nanotechnology, a brief classification of different approaches and applications, together with some sample cases

An Ecological Assessment of Property and Violent Crime Rates Across a Latino Urban Landscape: The Role of Social Disorganization and Institutional Anomie Theory

The present research put forth an integrated theoretical framework aimed at providing a more holistic community- level approach explaining crime across a heavily populated Latino city. Guided by social disorganization and institutional anomie theory, this study used several data sources and OLS regression techniques to examine the impact of social disorganization, economic and noneconomic institutional characteristics on rates of property and violent crime across 1,016 census block groups in San Antonio, Texas. While several findings emerged, interactions between alcohol density and concentrated disadvantage were significant and positively associated with property and violent crime. Interactions between welfare generosity and concentrated disadvantage were significant and negatively associated with the outcomes