English  |  正體中文  |  简体中文  |  Items with full text/Total items : 52507/87668 (60%)
Visitors : 9347718      Online Users : 183
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/89403

    Title: Maximal exponents of polyhedral cones (III)
    Authors: Raphael Loewy;Micha A. Perles;Tam, Bit-Shun
    Contributors: 淡江大學數學學系
    Date: 2013-07-01
    Issue Date: 2013-05-29 14:42:04 (UTC+8)
    Publisher: Providence: American Mathematical Society (AMS)
    Abstract: Let K be a proper (i.e., closed, pointed, full, convex) cone in Rn. An n × n matrix A is said to be K-primitive if AK ⊆ K and there exists a positive integer k such that Ak(K \ {0}) ⊆ intK; the least such k is referred to as the exponent of A and is denoted by γ(A). For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is denoted by γ(K). It is proved that for any positive integers m, n, 3 ≤ n ≤ m, the maximum value of γ(K), as K runs through all n-dimensional polyhedral cones with m extreme rays, equals (n−1)(m−1)+1/2(1+(−1)(n−1)m). For the 3-dimensional case, the cones K and the corresponding K-primitive matrices A such that γ(K) and γ(A) attain the maximum value are identified up to respectively linear isomorphism and cone-equivalence modulo positive scalar multiplication.
    Relation: Transactions of the American Mathematical Society 365(7), pp.3535-3573
    DOI: 10.1090/S0002-9947-2013-05879-5
    Appears in Collections:[數學學系暨研究所] 期刊論文

    Files in This Item:

    File Description SizeFormat

    All items in 機構典藏 are protected by copyright, with all rights reserved.

    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - Feedback