關鍵字查詢 | 類別:期刊論文 | | 關鍵字:Maximal exponents of polyhedral cones

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序號 學年期 教師動態
1 101/2 數學系 譚必信 教授 期刊論文 發佈 Maximal exponents of polyhedral cones (III) , [101-2] :Maximal exponents of polyhedral cones (III)期刊論文Maximal exponents of polyhedral cones (III)Raphael Loewy; Micha A. Perles; Tam, Bit-Shun淡江大學數學學系Providence: American Mathematical Society (AMS)Transactions of the American Mathematical Society 365(7), pp.3535-3573tku_id: ; 000043586;Submitted by 必信 譚 (bsm01@mail.tku.edu.tw) on 2013-05-29T06:42:03Z No. of bitstreams: 0;Made available in DSpace on 2013-05-29T06:42:04Z (GMT). No. of bitstreams: 0;20130603 verified by Sujenen_US0002-9947;1088-6850國外SCI;Tam, Bit-Shun是USA<links><record><name>機構典藏連結</name><url>http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/89403</url></record></links>
2 98/2 數學系 譚必信 教授 期刊論文 發佈 Maximal exponents of polyhedral cones (II) , [98-2] :Maximal exponents of polyhedral cones (II)期刊論文Maximal exponents of polyhedral cones (II)Raphael Loewy; Tam, Bit-Shun淡江大學數學學系Cone-preserving map; K-primitive matrix; Exponents; Polyhedral cone; Exp-maximal cone; Exp-maximal K-primitive matrix; Cone-equivalence; Minimal conePhiladelphia: Elsevier Inc.Linear Algebra and its Applications 432(11), pp.2861-2878100學年度研究獎補助論文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 there exists a positive integer k such that ; 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 called the exponent of K and is denoted by γ(K). It is proved that the maximum value of γ(K) as K runs through all n-dimensional minimal cones (i.e., cones having n+1 extreme rays) is n2-n+1 if n is odd, and is n2-n if n is even, the maximum value of the exponent being attained by a minimal cone with
3 98/2 數學系 譚必信 教授 期刊論文 發佈 Maximal exponents of polyhedral cones (I) , [98-2] :Maximal exponents of polyhedral cones (I)期刊論文Maximal exponents of polyhedral cones (I)Loewy, Raphael; Tam, Bit-Shun淡江大學數學學系Cone-preserving map; K-primitive matrix; Exponents; Polyhedral coneMaryland Heights: Academic PressJournal of Mathematical Analysis and Applications 365(2), pp.570-583Let 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 there exists a positive integer k such that Ak(K\{0}) ⊆ int K; 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 called the exponent of K and is denoted by γ(K). It is proved that if K is an n-dimensional polyhedral cone with m extreme rays then for any K-primitive matrix A, γ(A) ≦ (mA − 1)(m − 1) + 1, where mA denotes the degree of the minimal polynomial of A, and the equality holds only if the digraph (E,P(A,K)) associated with A (as a cone-preserving map) is equal to th
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