Alexander Invariants of Complex Hyperplane Arrangements

Let A be an arrangement of complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism from a finitely generated free group to the pure braid group. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of A. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of A. We also provide a combinatorial criterion for when these lower bounds are attained.Comment: 26 pages; LaTeX2e with amscd, amssymb package

Characteristic varieties of arrangements

The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of V_k(A). For any arrangement A, we show that the tangent cone at the identity of this variety coincides with R^1_k(A), one of the cohomology support loci of the Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all positive-dimensional components of V_k(A) are combinatorially determined, and that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving a conjecture of Falk. We use these results to study the reflection arrangements associated to monomial groups.Comment: LaTeX2e, 20 pages. A reference to Libgober's recent work in math.AG/9801070 is added. Several points are clarified, a new example is include

The boundary manifold of a complex line arrangement

We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander polynomial associated to the abelianization of G and an arbitrary complex representation. We give an explicit description of the unit ball in the Alexander norm, and use it to analyze certain Bieri-Neumann-Strebel invariants of G. From the Alexander polynomial, we also obtain a complete description of the first characteristic variety of G. Comparing this with the corresponding resonance variety of the cohomology ring of G enables us to characterize those arrangements for which the boundary manifold is formal.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Valence-band satellite in the ferromagnetic nickel: LDA+DMFT study with exact diagonalization

The valence-band spectrum of the ferromagnetic nickel is calculated using the LDA+DMFT method. The auxiliary impurity model emerging in the course of the calculations is discretized and solved with the exact diagonalization, or, more precisely, with the Lanczos method. Particular emphasis is given to spin dependence of the valence-band satellite that is observed around 6 eV below the Fermi level. The calculated satellite is strongly spin polarized in accord with experimental findings.Comment: REVTeX 4, 8 pages, 5 figure

Orbital magnetic moment and extrinsic spin Hall effect for iron impurity in gold

We report electronic structure calculations of an iron impurity in gold host. The spin, orbital and dipole magnetic moments were investigated using the LDA+$U$ correlated band theory. We show that the {\em around-mean-field}-LDA+$U$ reproduces the XMCD experimental data well and does not lead to formation of a large orbital moment on the Fe atom. Furthermore, exact diagonalization of the multi-orbital Anderson impurity model with the full Coulomb interaction matrix and the spin-orbit coupling is performed in order to estimate the spin Hall angle. The obtained value $\gamma_S \approx 0.025$ suggests that there is no giant extrinsic spin Hall effect due to scattering on iron impurities in gold.Comment: 5 pages, 2 figure

Question-answering, relevance feedback and summarisation : TREC-9 interactive track report

In this paper we report on the effectiveness of query-biased summaries for a question-answering task. Our summarisation system presents searchers with short summaries of documents, composed of a series of highly matching sentences extracted from the documents. These summaries are also used as evidence for a query expansion algorithm to test the use of summaries as evidence for interactive and automatic query expansion

Thermodynamic consistency of the charge response in dynamical mean-field based approaches

We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here, maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.Comment: 11 pages (incl. appendix), 4 figure

History of Discovery and Development of Woodbine Oil Fields in East Texas

The purpose of this paper is to present a brief historical summary of the discovery and development of the Woodbine oil fields of East Texas. A simple listing, or tabulation of the Woodbine oil fields, with discovery dates, would be dry reading, indeed, so I will try to review the history of this important oil producing formation and area as a story - a story of lines or trends of geological thought, of lease plays and exploratory operations resulting from these lines or trends of thought; and of the changes in geological thought resulting from some of the more important developments. From a strictly historical viewpoint, two dates stand out through the perspective of the years as of primary significance. The first of these is October, 1920, when the first Woodbine oil was brought to the surface of the ground, at Mexia. The second is March, 1927, the completion date of the discovery well of the Boggy Creek field. Mexia, of course, rates as a major discovery by any standard; of the Woodbine oil fields, only Powell, Van, East Texas and Hawkins have produced, or seem likely to produce more oil. Boggy Creek, on the other hand, ranks low in any statistical evaluation, but as I hope to demonstrate later, is second only to Mexia in historical importance