948 research outputs found

    Middle Convolution and Harnad Duality

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    We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.Comment: 50 pages; v2: Submitted version once revised according to referees' comment

    RSPO1/beta-Catenin Signaling Pathway Regulates Oogonia Differentiation and Entry into Meiosis in the Mouse Fetal Ovary

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    Differentiation of germ cells into male gonocytes or female oocytes is a central event in sexual reproduction. Proliferation and differentiation of fetal germ cells depend on the sex of the embryo. In male mouse embryos, germ cell proliferation is regulated by the RNA helicase Mouse Vasa homolog gene and factors synthesized by the somatic Sertoli cells promote gonocyte differentiation. In the female, ovarian differentiation requires activation of the WNT/β-catenin signaling pathway in the somatic cells by the secreted protein RSPO1. Using mouse models, we now show that Rspo1 also activates the WNT/β-catenin signaling pathway in germ cells. In XX Rspo1(−/−) gonads, germ cell proliferation, expression of the early meiotic marker Stra8, and entry into meiosis are all impaired. In these gonads, impaired entry into meiosis and germ cell sex reversal occur prior to detectable Sertoli cell differentiation, suggesting that β-catenin signaling acts within the germ cells to promote oogonial differentiation and entry into meiosis. Our results demonstrate that RSPO1/β-catenin signaling is involved in meiosis in fetal germ cells and contributes to the cellular decision of germ cells to differentiate into oocyte or sperm

    Conductivity of 2D many-component electron gas, partially-quantized by magnetic field

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    The 2D semimetal consisting of heavy holes and light electrons is studied. The consideration is based on assumption that electrons are quantized by magnetic field while holes remain classical. We assume also that the interaction between components is weak and the conversion between components is absent. The kinetic equation for holes colliding with quantized electrons is utilized. It has been stated that the inter-component friction and corresponding correction to the dissipative conductivity σxx\sigma_{xx} {\it do not vanish at zero temperature} due to degeneracy of the Landau levels. This correction arises when the Fermi level crosses the Landau level. The limits of kinetic equation applicability were found. We also study the situation of kinetic memory when particles repeatedly return to the points of their meeting.Comment: 13 pages, 1 figur

    Proton Radiative Capture at E_p = 150 MeV

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    This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

    Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

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    In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator P\mathbf{P} consisting of finitely or countably many distributional operators PnP_n, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function GG with respect to L:=P∗TPL:=\mathbf{P}^{\ast T}\mathbf{P} now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator P∗\mathbf{P}^{\ast} of P\mathbf{P} is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function GG can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant sf,Xs_{f,X} to data values sampled from an unknown generalized Sobolev function ff at data sites located in some set X⊂RdX \subset \mathbb{R}^d. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator P\mathbf{P}. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

    Implementation of a medium-modified parton shower algorithm

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    We present a Monte Carlo implementation of medium-induced gluon radiation in the final-state branching process. Medium effects are introduced through an additive term in the splitting functions. We have implemented such modification within PYTHIA. We show the medium effects on the hump-backed plateau, and the transverse momentum and angular distributions with respect to the parent parton. As expected, with increasing medium densities there is an increase (decrease) of partons with small (large) momentum fraction, and angular broadening is observed. The effects on the transverse-momentum distributions are more involved, with an enhancement of low- and intermediate-pTp_T partons and a decrease at large pTp_T, which is related to energy conservation, and to the lack of momentum exchange with the medium in our approach.Comment: LaTeX, 6 pages, 2 eps figures; proceedings of the 3rd International Conference on Hard and Electromagnetic Probes in High-Energy Nuclear Collisions - Hard Probes 2008 (Illa de A Toxa, Spain, June 8th-14th 2008
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