42,916 research outputs found

    A visual analysis of the usage efficiency of library books

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    The monographic collections in academic libraries have undergone a period of tremendous growth in volume, in subject diversity, and in formats during the recent several decades. Readers may find it difficult to prioritize which book(s) should be borrowed for a specific purpose. The log data of book loan record may serve as a visible indicator for the more sought-after books by the readers. This paper describes our experimental efforts in works in a university library setting. The visual analysis is thought to provide an effective way to extract the book usage information, which may yield new insights into a host of other related technical as well as user behavior issues. Initial experiment has demonstrated that the proposed approach as articulated in this article can actually benefit end-users as well as library collection development personnel in their endeavor of book selections with effective measure.</p

    Some remarks on circle action on manifolds

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    This paper contains several results concerning circle action on almost-complex and smooth manifolds. More precisely, we show that, for an almost-complex manifold M2mnM^{2mn}(resp. a smooth manifold N4mnN^{4mn}), if there exists a partition λ=(λ1,...,λu)\lambda=(\lambda_{1},...,\lambda_{u}) of weight mm such that the Chern number (cλ1...cλu)n[M](c_{\lambda_{1}}... c_{\lambda_{u}})^{n}[M] (resp. Pontrjagin number (pλ1...pλu)n[N](p_{\lambda_{1}}... p_{\lambda_{u}})^{n}[N]) is nonzero, then \emph{any} circle action on M2mnM^{2mn} (resp. N4mnN^{4mn}) has at least n+1n+1 fixed points. When an even-dimensional smooth manifold N2nN^{2n} admits a semi-free action with isolated fixed points, we show that N2nN^{2n} bounds, which generalizes a well-known fact in the free case. We also provide a topological obstruction, in terms of the first Chern class, to the existence of semi-free circle action with \emph{nonempty} isolated fixed points on almost-complex manifolds. The main ingredients of our proofs are Bott's residue formula and rigidity theorem.Comment: 10 pages,to appear in Mathematical Research Letter

    Circle action and some vanishing results on manifolds

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    Kawakubo and Uchida showed that, if a closed oriented 4k4k-dimensional manifold MM admits a semi-free circle action such that the dimension of the fixed point set is less than 2k2k, then the signature of MM vanishes. In this note, by using GG-signature theorem and the rigidity of the signature operator, we generalize this result to more general circle actions. Combining the same idea with the remarkable Witten-Taubes-Bott rigidity theorem, we explore more vanishing results on spin manifolds admitting such circle actions. Our results are closely related to some earlier results of Conner-Floyd, Landweber-Stong and Hirzebruch-Slodowy.Comment: 7 pages, typos corrected and minors modifie

    On an algebraic formula and applications to group action on manifolds

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    We consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound of the number of fixed points. We also give an obstruction to the existence of Zp\mathbb{Z}_p action on manifolds with isolated fixed points when pp is a prime.Comment: 7 pages, revised slightly to update a new reference and reassign the credit of the idea in this not

    Regenesis and quantum traversable wormholes

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    Recent gravity discussions of a traversable wormhole indicate that in holographic systems signals generated by a source could reappear long after they have dissipated, with the need of only performing some simple operations. In this paper we argue the phenomenon, to which we refer as "regenesis", is universal in general quantum chaotic many-body systems, and elucidate its underlying physics. The essential elements behind the phenomenon are: (i) scrambling which in a chaotic system makes out-of-time-ordered correlation functions (OTOCs) vanish at large times; (ii) the entanglement structure of the state of the system. The latter aspect also implies that the regenesis phenomenon requires fine tuning of the initial state. Compared to other manifestations of quantum chaos such as the initial growth of OTOCs which deals with early times, and a random matrix-type energy spectrum which reflects very large time behavior, regenesis concerns with intermediate times, of order the scrambling time of a system. We also study the phenomenon in detail in general two-dimensional conformal field theories in the large central charge limit, and highlight some interesting features including a resonant enhancement of regenesis signals near the scrambling time and their oscillations in coupling. Finally, we discuss gravity implications of the phenomenon for systems with a gravity dual, arguing that there exist regimes for which traversability of a wormhole is quantum in nature, i.e. cannot be associated with a semi-classical spacetime causal structure
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