| 释义 |
hypercyclic, a.|ˌhaɪpəˈsaɪklɪk|
[f. hyper- 3 a + cyclic a.]
1. Algebra. Of a group: containing a nested series of normal subgroups of which the smallest is trivial, such that the quotient groups of consecutive pairs in this series are all cyclic. Also applied to other mathematical entities having similar properties.
1968W. H. Caldwell in Pacific Jrnl. Math. XXIV. 29 The object of this paper is to provide characterizations for certain rings R having the property that each cyclic right R-module has a cyclic injective hull. Such rings will be called hypercyclic. 1969U. Schoenwaelder in Ibid. XXXI. 198 A group G is called hypercyclic, if every epimorphic image, not 1, of G has a cyclic, normal subgroup, not 1. 1975Mathematische Zeitschr. CXLIV. 283 A group G is hypercyclic if and only if G has an ascending series 1 = G0 {Csub} G1 {Csub}... {Csub} Gλ {Csub} Gλ+1 {Csub}... {Csub} Gp = G of normal subgroups Gλ such that for ordinals λ, which are not limit ordinals, Gλ/Gλ-1 is a cyclic group. 1988Archiv der Math. LI. 13 For minimax groups the properties ‘locally nilpotent’, ‘locally supersoluble’ and ‘locally FC-nilpotent’ coincide with the properties ‘hypercentral’, ‘hypercyclic’ and ‘FC-nilpotent’, respectively.
2. Math. Of the nature of or consisting of a hypercycle or hypercycles (*hypercycle n. 2).
1977Naturwissenschaften LXIV. 541/2 Only hypercyclic organizations are able to fulfil these requirements. 1981Sci. Amer. Apr. 86/2 In a hypercyclic system a closed loop of catalytic couplings connects self-replicative cycles. 1986Jrnl. Theoret. Biol. CXVIII. 3 The hypercycle..can be unstable when the fluctuations are anomalously enhanced under the influence of environmental fluctuations on the hypercyclic organization. |