Holomorphic Hulls and Holomorphic Convexity

Paper by R. O. Wells, Jr

Automorphic Cohomology on Homogeneous Complex Manifolds

Paper by R. O. Wells, Jr

Recent advances in wavelet technology

Wavelet research has been developing rapidly over the past five years, and in particular in the academic world there has been significant activity at numerous universities. In the industrial world, there has been developments at Aware, Inc., Lockheed, Martin-Marietta, TRW, Kodak, Exxon, and many others. The government agencies supporting wavelet research and development include ARPA, ONR, AFOSR, NASA, and many other agencies. The recent literature in the past five years includes a recent book which is an index of citations in the past decade on this subject, and it contains over 1,000 references and abstracts

Analysis of wavelet technology for NASA applications

The purpose of this grant was to introduce a broad group of NASA researchers and administrators to wavelet technology and to determine its future role in research and development at NASA JSC. The activities of several briefings held between NASA JSC scientists and Rice University researchers are discussed. An attached paper, 'Recent Advances in Wavelet Technology', summarizes some aspects of these briefings. Two proposals submitted to NASA reflect the primary areas of common interest. They are image analysis and numerical solutions of partial differential equations arising in computational fluid dynamics and structural mechanics

The Envelope of Holomorphy of a Two-Manifold in C2

Paper by L. R. Hunt and R. O. Wells, Jr

Twistor Bundles, Einstein Equations and Real Structures

We consider sphere bundles P and P' of totally null planes of maximal dimension and opposite self-duality over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP' of P and P' is found to be appropriate for the encoding of both the selfdual and the Einstein-Weyl equations for the 4-metric. This encoding is realized in terms of the properties of certain well defined geometrical objects on PP'. The formulation is suitable for both complex- and real-valued metrics. It unifies results for all three possible real signatures. In the purely Riemannian positive definite case it implies the existence of a natural almost hermitian structure on PP' whose integrability conditions correspond to the self-dual Einstein equations of the 4-metric. All Einstein equations for the 4-metric are also encoded in the properties of this almost hermitian structure on PP'.Comment: Paper accepted in Classical and Quantum Gravity, Special issue in honour of Professor Andrzej Trautma

The high-pressure phase of boron, {\gamma}-B28: disputes and conclusions of 5 years after discovery

{\gamma}-B28 is a recently established high-pressure phase of boron. Its structure consists of icosahedral B12 clusters and B2 dumbbells in a NaCl-type arrangement (B2){\delta}+(B12){\delta}- and displays a significant charge transfer {\delta}~0.5- 0.6. The discovery of this phase proved essential for the understanding and construction of the phase diagram of boron. {\gamma}-B28 was first experimentally obtained as a pure boron allotrope in early 2004 and its structure was discovered in 2006. This paper reviews recent results and in particular deals with the contentious issues related to the equation of state, hardness, putative isostructural phase transformation at ~40 GPa, and debates on the nature of chemical bonding in this phase. Our analysis confirms that (a) calculations based on density functional theory give an accurate description of its equation of state, (b) the reported isostructural phase transformation in {\gamma}-B28 is an artifact rather than a fact, (c) the best estimate of hardness of this phase is 50 GPa, (d) chemical bonding in this phase has a significant degree of ionicity. Apart from presenting an overview of previous results within a consistent view grounded in experiment, thermodynamics and quantum mechanics, we present new results on Bader charges in {\gamma}-B28 using different levels of quantum-mechanical theory (GGA, exact exchange, and HSE06 hybrid functional), and show that the earlier conclusion about significant degree of partial ionicity in this phase is very robust

Critical Josephson Current in a Model Pb/YBa_2Cu_3O_7 Junction

In this article we consider a simple model for a c--axis Pb/YBa_2Cu_3O_{7-\delta} Josephson junction. The observation of a nonzero current in such a junction by Sun et al. [A. G. Sun, D. A. Gajewski, M. B. Maple, R. C. Dynes, Phys. Rev. Lett. 72, 2267 (1994)] has been taken as evidence against d--wave superconductivity in YBa_2Cu_3O_{7-\delta}. We suggest, however, that the pairing interaction in the CuO_2 planes may well be d--wave but that the CuO chains destroy the tetragonal symmetry of the system. We examine two ways in which this happens. In a simple model of an incoherent junction, the chains distort the superconducting condensate away from d_{x^2-y^2} symmetry. In a specular junction the chains destroy the tetragonal symmetry of the tunneling matrix element. In either case, the loss of tetragonal symmetry results in a finite Josephson current. Our calculated values of the critical current for specular junctions are in good agreement with the results of Sun and co-workers.Comment: Latex File, 21 pages, 6 figures in uuencoded postscript, In Press (Phys. Rev. B

Ancient Migratory Events in the Middle East: New Clues from the Y-Chromosome Variation of Modern Iranians

Knowledge of high resolution Y-chromosome haplogroup diversification within Iran provides important geographic context regarding the spread and compartmentalization of male lineages in the Middle East and southwestern Asia. At present, the Iranian population is characterized by an extraordinary mix of different ethnic groups speaking a variety of Indo-Iranian, Semitic and Turkic languages. Despite these features, only few studies have investigated the multiethnic components of the Iranian gene pool. In this survey 938 Iranian male DNAs belonging to 15 ethnic groups from 14 Iranian provinces were analyzed for 84 Y-chromosome biallelic markers and 10 STRs. The results show an autochthonous but non-homogeneous ancient background mainly composed by J2a sub-clades with different external contributions. The phylogeography of the main haplogroups allowed identifying post-glacial and Neolithic expansions toward western Eurasia but also recent movements towards the Iranian region from western Eurasia (R1b-L23), Central Asia (Q-M25), Asia Minor (J2a-M92) and southern Mesopotamia (J1-Page08). In spite of the presence of important geographic barriers (Zagros and Alborz mountain ranges, and the Dasht-e Kavir and Dash-e Lut deserts) which may have limited gene flow, AMOVA analysis revealed that language, in addition to geography, has played an important role in shaping the nowadays Iranian gene pool. Overall, this study provides a portrait of the Y-chromosomal variation in Iran, useful for depicting a more comprehensive history of the peoples of this area as well as for reconstructing ancient migration routes. In addition, our results evidence the important role of the Iranian plateau as source and recipient of gene flow between culturally and genetically distinct population