8,727 research outputs found

    The projective translation equation and unramified 2-dimensional flows with rational vector fields

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    Let X=(x,y). Previously we have found all rational solutions of the 2-dimensional projective translation equation, or PrTE, (1-z)f(X)=f(f(Xz)(1-z)/z); here f(X)=(u(x,y),v(x,y)) is a pair of two (real or complex) functions. Solutions of this functional equation are called projective flows. A vector field of a rational flow is a pair of 2-homogenic rational functions. On the other hand, only special pairs of 2-homogenic rational functions give rise to rational flows. In this paper we are interested in all non-singular (satisfying the boundary condition) and unramified (without branching points, i.e. single-valued functions in C^2\{union of curves}) projective flows whose vector field is still rational. We prove that, up to conjugation with 1-homogenic birational plane transformation, these are of 6 types: 1) the identity flow; 2) one flow for each non-negative integer N - these flows are rational of level N; 3) the level 1 exponential flow, which is also conjugate to the level 1 tangent flow; 4) the level 3 flow expressable in terms of Dixonian (equianharmonic) elliptic functions; 5) the level 4 flow expressable in terms of lemniscatic elliptic functions; 6) the level 6 flow expressable in terms of Dixonian elliptic functions again. This reveals another aspect of the PrTE: in the latter four cases this equation is equivalent and provides a uniform framework to addition formulas for exponential, tangent, or special elliptic functions (also addition formulas for polynomials and the logarithm, though the latter appears only in branched flows). Moreover, the PrTE turns out to have a connection with Polya-Eggenberger urn models. Another purpose of this study is expository, and we provide the list of open problems and directions in the theory of PrTE; for example, we define the notion of quasi-rational projective flows which includes curves of arbitrary genus.Comment: 34 pages, 2 figure

    The Warm Absorber constrained by the coronal lines in Seyfert 1 galaxies

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    We present results of the photoionization code IRIS, which calculates the spectrum emitted by the Warm Absorber (WA) in Seyfert 1 galaxies for a large grid of parameters (density, column density, ionization parameter...). We show that in Seyfert 1s, coronal lines ([Fe X], [Fe XI], [Fe XIV]...), unlike the absorption edges, such as those of O VII and O VIII observed in soft X-rays which are produced by the WA, strongly constrain the physical parameters of the WA, especially the hydrogen density. Indeed, in order to avoid producing coronal line equivalent widths larger than observed, a high density ($n_{H} models (photoionized medium in or out of thermal equilibrium). This result is obtained for the mean observed Seyfert 1 features, as well as for the case study of MCG-6-30-15. It implies that the distance of the WA from the incident radiation source is of the order of that of the Broad Line Region (BLR)

    Polycistronic Delivery of IL-10 and NT-3 Promotes Oligodendrocyte Myelination and Functional Recovery in a Mouse Spinal Cord Injury Model.

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    One million estimated cases of spinal cord injury (SCI) have been reported in the United States and repairing an injury has constituted a difficult clinical challenge. The complex, dynamic, inhibitory microenvironment postinjury, which is characterized by proinflammatory signaling from invading leukocytes and lack of sufficient factors that promote axonal survival and elongation, limits regeneration. Herein, we investigated the delivery of polycistronic vectors, which have the potential to coexpress factors that target distinct barriers to regeneration, from a multiple channel poly(lactide-co-glycolide) (PLG) bridge to enhance spinal cord regeneration. In this study, we investigated polycistronic delivery of IL-10 that targets proinflammatory signaling, and NT-3 that targets axonal survival and elongation. A significant increase was observed in the density of regenerative macrophages for IL-10+NT-3 condition relative to conditions without IL-10. Furthermore, combined delivery of IL-10+NT-3 produced a significant increase of axonal density and notably myelinated axons compared with all other conditions. A significant increase in functional recovery was observed for IL-10+NT-3 delivery at 12 weeks postinjury that was positively correlated to oligodendrocyte myelinated axon density, suggesting oligodendrocyte-mediated myelination as an important target to improve functional recovery. These results further support the use of multiple channel PLG bridges as a growth supportive substrate and platform to deliver bioactive agents to modulate the SCI microenvironment and promote regeneration and functional recovery. Impact statement Spinal cord injury (SCI) results in a complex microenvironment that contains multiple barriers to regeneration and functional recovery. Multiple factors are necessary to address these barriers to regeneration, and polycistronic lentiviral gene therapy represents a strategy to locally express multiple factors simultaneously. A bicistronic vector encoding IL-10 and NT-3 was delivered from a poly(lactide-co-glycolide) bridge, which provides structural support that guides regeneration, resulting in increased axonal growth, myelination, and subsequent functional recovery. These results demonstrate the opportunity of targeting multiple barriers to SCI regeneration for additive effects

    Cultures of caste and rural development in the social network of a south Indian village

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    Cultures of caste in much of rural India have become entangled with institutions of rural development. In community-driven development, emphasis on “local resource persons” and “community spokespersons” has created new opportunities for brokerage and patronage within some villages, which interact with existing forms of authority and community afforded by caste identity and intra-caste headmanship. In this article, we study how these entangled cultures of caste and development translate into social network structures using data on friendship ties from a south Indian village. We find that although caste continues to be important in shaping community structures and leadership in the village’s network, its influence varies across different communities. This fluidity of caste’s influence on community network structures is argued to be the result of multiple distinct yet partially overlapping cultural-political forces, which include sharedness afforded by caste identity and new forms of difference and inequality effected through rural development

    The line parameters and ratios as the physical probe of the line emitting regions in AGN

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    Here we discuss the physical conditions in the emission line regions (ELR) of active galactic nuclei (AGN), with the special emphasize on the unresolved problems, e.g. the stratification of the Broad Line Region (BLR) or the failure of the photoionization to explain the strong observed optical Fe II emission. We use here different line fluxes in order to probe the properties of the ELR, such as the hydrogen Balmer lines (Ha to He), the helium lines from two subsequent ionization levels (He II 4686 and He I 5876) and the strongest Fe II lines in the wavelength interval 4400-5400 \AA. We found that the hydrogen Balmer and helium lines can be used for the estimates of the physical parameters of the BLR, and we show that the Fe II emission is mostly emitted from an intermediate line region (ILR), that is located further away from the central continuum source than the BLR.Comment: 8 pages, 9 figures, 2 tables, New Astronomy Reviews (Proceeding of 7th SCSLSA), in pres

    Monitoring spatial and temporal variations of surface albedo on Saint Sorlin Glacier (French Alps) using terrestrial photography

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    Accurate knowledge of temperate glacier mass balance is essential to understand the relationship between glacier and climate. Defined as the reflected fraction of incident radiation over the whole solar spectrum, the surface broadband albedo is one of the most important variable in a glacier's mass balance. This study presents a new method to retrieve the albedo of frozen surfaces from terrestrial photography at visible and near infrared wavelengths. This method accounts for the anisotropic reflectance of snow and ice surfaces and uses a radiative transfer model for narrow-to-broadband conversion. The accuracy of the method was assessed using concomitant measurements of albedo during the summers 2008 and 2009 on Saint Sorlin Glacier (Grandes Rousses, France). These albedo measurements are performed at two locations on the glacier, one in the ablation area and the other in the accumulation zone, with a net radiometer Kipp and Zonen CNR1. The main sources of uncertainty are associated with the presence of high clouds and the georeferencing of the photographs
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