Volume and Area Renormalizations for Conformally Compact Einstein Metrics

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory correspondence.Comment: 15 pages, to appear Proc. of 19th Winter School in Geometry and Physics, Srni, Czech Rep., Jan. 199

Racial Identity Among Mixed Adolescents in Hawaii: A Research Note

The islands of Hawaii are well-known for their unique level of racial heterogeneity and admixture, overt norms of racial tolerance and harmony, and temperate climate. Of central interest to the social scientist is the manner in which racial and cultural blending take place in such a complex society, particularly among those of mixed racial origin; Hawaii provides a social laboratory in which to study such processes in depth. This paper, viewing racial identity as an important index of intergroup relations, examines the racial identities and related reasons of forty high school adolescents in Hawaii in order to highlight controlling factors of the social environment

Jet isomorphism for conformal geometry

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi.Comment: 29 pages, based on lectures delivered at the 2007 Winter School 'Geometry and Physics', Srni, Czech Republic; v.2 corrects typos introduced by arXiv HyperTeX macr

Conformal Powers of the Laplacian via Stereographic Projection

A new derivation is given of Branson's factorization formula for the conformally invariant operator on the sphere whose principal part is the k-th power of the scalar Laplacian. The derivation deduces Branson's formula from knowledge of the corresponding conformally invariant operator on Euclidean space (the k-th power of the Euclidean Laplacian) via conjugation by the stereographic projection mapping.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The quest for extreme water repellency: Superhydrophobicity made easy

In his seminal work On Floating Bodies I Archimedes of Syracuse provided an explanation of the action of solid bodies on water. Although his thesis immediately benefitted King Heiro II² and has continued to serve mankind well, it ignores the effect of the interfacial interactions between the solid, water and air (surface tension). These interactions are negligible, or at least are considered negligible, compared to forces arising from the effect of gravity on large bodies. However, as the mass of the body decreases, the surface interactions become increasingly important leading to some unusual and potentially useful phenomena. The understanding and application of these effects is currently driving much fundamental research by physicists, chemical engineers, material scientists, and chemists into surfaces that display extreme properties, in particular extreme water repellency, or superhydrophobicitv. It is only comparatively recently that detailed mathematical expressions for the interaction between a liquid, solid and gas at these extremes have been developed, making progress that parallels that for the fabrication of these surfaces

On the importance of π–π stacking and cation–anion interactions in the construction of non-centrosymmetric networks of bromide salts of imidazolium cations bearing arene and polyfluoroarene rings

The salt 1-(2,3,5,6-tetrafluoropyridyl)-3-benzylimidazolium bromide crystallizes in the non-centrosymmetric space group Pna2₁. The structure arises from π–π stacking between the benzyl and tetrafluoropyridyl groups of the cations and cation–bromide interactions. It is the latter that gives rise to the non-centrosymmetry