1,627 research outputs found

    Approximation of conformal mappings by circle patterns

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    A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0,π)(0,\pi). Two sequences of circle patterns are employed to approximate a given conformal map gg and its first derivative. For the domain of gg we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of gg' (g|g'| or argg\arg g'). For quasicrystallic circle patterns the convergence result is strengthened to CC^\infty-convergence on compact subsets.Comment: 36 pages, 7 figure

    Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit

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    Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulae for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a non trivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional non equatorial images may play an important role in the phenomenology.Comment: 13 pages, 9 figures. Improved version with detailed physical discussio

    Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

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    In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel and Xu, and the framework established by Carter and Quintana the post Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces also the outer surface boundary conditions are presented. The PN junction condition is an extension of Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page

    Identification of differentially expressed small non-coding RNAs in the legume endosymbiont Sinorhizobium meliloti by comparative genomics

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    Bacterial small non-coding RNAs (sRNAs) are being recognized as novel widespread regulators of gene expression in response to environmental signals. Here, we present the first search for sRNA-encoding genes in the nitrogen-fixing endosymbiont Sinorhizobium meliloti, performed by a genome-wide computational analysis of its intergenic regions. Comparative sequence data from eight related α-proteobacteria were obtained, and the interspecies pairwise alignments were scored with the programs eQRNA and RNAz as complementary predictive tools to identify conserved and stable secondary structures corresponding to putative non-coding RNAs. Northern experiments confirmed that eight of the predicted loci, selected among the original 32 candidates as most probable sRNA genes, expressed small transcripts. This result supports the combined use of eQRNA and RNAz as a robust strategy to identify novel sRNAs in bacteria. Furthermore, seven of the transcripts accumulated differentially in free-living and symbiotic conditions. Experimental mapping of the 5′-ends of the detected transcripts revealed that their encoding genes are organized in autonomous transcription units with recognizable promoter and, in most cases, termination signatures. These findings suggest novel regulatory functions for sRNAs related to the interactions of α-proteobacteria with their eukaryotic hosts

    Unravelling an allochthonous, subaqueously-deposited volcanic-epiclastic to subaerial andesitic lava assemblage in Hong Kong: age, stratigraphy and provenance studies of the Middle Jurassic Tuen Mun Formation

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    The Middle Jurassic Tuen Mun Formation, Hong Kong, is a fault-bounded block of rare andesitic and related rocks that preserve a snapshot of the developing SE China continental arc system during the late Mesozoic. The forearc depositional setting is considered to have been dominated by an emergent andesitic volcanic massif, which shows a transition to a fluvialdominated volcanic plain, and then to an offshore marine environment. The youngest laser ablation inductively coupled plasma mass spectrometry U–Pb detrital zircon ages obtained from the three packages define a coherent group (n = 396; MSWD = 1.8) suggesting a maximum depositional age of 169.5 ± 0.3 Ma. The dominance of large euhedral and concentrically zoned zircons reflects a common volcanic provenance. Hf isotope data (εHf(t) = 0 to −11) on the youngest representative zircon grains imply derivation of magmas from dominantly recycled crustal sources. The detrital zircon age signatures and Hf isotope data show no indication of magmatic interaction with adjacent late Palaeozoic and Early to Middle Jurassic sedimentary rocks, or Middle Jurassic to Early Cretaceous magmatic rocks of Hong Kong. On the basis of the structural, zircon age and isotope data, the Tuen Mun Formation is interpreted to be an allochthonous block, emplaced in the Hong Kong region during the late Middle Jurassic

    Neutron Scattering Study of Crystal Field Energy Levels and Field Dependence of the Magnetic Order in Superconducting HoNi2B2C

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    Elastic and inelastic neutron scattering measurements have been carried out to investigate the magnetic properties of superconducting (Tc~8K) HoNi2B2C. The inelastic measurements reveal that the lowest two crystal field transitions out of the ground state occurat 11.28(3) and 16.00(2) meV, while the transition of 4.70(9) meV between these two levels is observed at elevated temperatures. The temperature dependence of the intensities of these transitions is consistent with both the ground state and these higher levels being magnetic doublets. The system becomes magnetically long range ordered below 8K, and since this ordering energy kTN ~ 0.69meV << 11.28meV the magnetic properties in the ordered phase are dominated by the ground-state spin dynamics only. The low temperature structure, which coexists with superconductivity, consists of ferromagnetic sheets of Ho{3+ moments in the a-b plane, with the sheets coupled antiferromagnetically along the c-axis. The magnetic state that initially forms on cooling, however, is dominated by an incommensurate spiral antiferromagnetic state along the c-axis, with wave vector qc ~0.054 A-1, in which these ferromagnetic sheets are canted from their low temperature antiparallel configuration by ~17 deg. The intensity for this spiral state reaches a maximum near the reentrant superconducting transition at ~5K; the spiral state then collapses at lower temperature in favor of the commensurate antiferromagnetic state. We have investigated the field dependence of the magnetic order at and above this reentrant superconducting transition. Initially the field rotates the powder particles to align the a-b plane along the field direction, demonstrating that the moments strongly prefer to lie within this plane due to the crystal field anisotropy. Upon subsequently increasing the field atComment: RevTex, 7 pages, 11 figures (available upon request); Physica

    Carbono orgânico dissolvido e biodisponibilidade de N e P como indicadores de qualidade do solo

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    Nas últimas décadas, qualidade do solo tem se tornado um tópico importante na ciência do solo. Embora esforços consideráveis tenham sido dedicados com o intuito de definir "qualidade do solo", ainda não há um conceito amplamente aceito pela comunidade cientifica. A seleção de índices qualitativos para definir qualidade do solo é uma tarefa extremamente difícil, e diversas propriedades químicas, físicas e biológicas tem sido sugeridas como potenciais indicadores. A matéria orgânica do solo está associada com processos químicos, físicos e biológicos no solo, e, portanto, é considerada um dos melhores indicadores de qualidade do solo. O manejo do solo pode influenciar significativamente a dinâmica do carbono orgânico e o ciclo de N, P, e S. Entretanto, mudanças na concentração total da matéria organica em resposta ao manejo pode ser dificil de ser detectada devido à variabilidade natural do solo. Quando comparada com a matéria orgânica total do solo, a fração mais prontamente disponível, como o carbono orgânico dissolvido (COD), é mais sensível às mudanças no manejo do solo a curto e médio prazo e, portanto, pode ser utilizada como indicador fundamental de qualidade do solo ou das alterações das condições naturais. Embora a fração dissolvida represente apenas uma pequena porção da matéria orgânica total do solo, o COD é móvel no solo e constitui uma importante fonte de C para os microorganismos, podendo facilmente refletir os efeitos de diferentes sistemas de manejo. Inúmeros métodos são utilizados para caracterizar o COD, mas os processos que influenciam sua mineralização e a disponibilidade dos elementos associado com a matéria orgânica (N, P, e S) ainda não são completamente entendidos. Pesquisas futuras devem buscar entender os processos que governam a dinâmica de nutrientes e do COD e como os mesmos afetam a qualidade do solo.Soil quality has become an important issue in soil science. Considerable attempts have been made to define soil quality, but a general concept has not yet been accepted by the scientific community. The selection of quantitative indices for soil quality is extremely difficult, and a considerable number of chemical, physical, and biochemical properties have been suggested as potential indicators of soil quality. Because soil organic matter (SOM) can be associated with different soil chemical, physical and biological processes, it has been widely considered as one of the best soil quality indicator. Land use can significantly influence dynamics of organic carbon and N, P, and S cycle. However, changes in total soil organic carbon (SOC) contents in response to land use may be difficult to detect because of the natural soil variability. In the short to medium term, biological properties and readily decomposable fractions of SOC, such as dissolved organic carbon (DOC), are much more sensitive to soil management than is SOM as a whole, and can be used as a key indicator of soil natural functions. Despite the fact that labile C accounts for a small portion of the total organic matter in the soils, DOC is the most mobile and important C-source for microorganisms, and can easily reflect the effects of land use on soil quality. Although several methods are used to characterize DOC, the factors influencing mineralization and bioavailability of elements associated with organic matter (N, P, and S) remains unclear. Future research should focus on the processes that govern DOC and nutrient dynamics and how they affect soil quality

    Theoretical study of electronic Raman scattering of Borocarbide superconductors

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    The electronic Raman scattering of Borocarbide superconductors is studied based on the weak coupling theory with s+gs+g-wave gap symmetry. The low energy behaviors and the relative peak positions can be naturally understood, while the explanation of the detailed shape of the B1gB_{1g} peak seems to require a strong inelastic interaction not present in the weak coupling theory.Comment: Revtex 4 file, 9 pages and 5 figure
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