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Variational principle and zero temperature limits of asymptotically (sub)-additive projection pressure
Qiuhong WANG, Yun ZHAO
Front. Math. China. 2018, 13 (5): 1099-1120.
https://doi.org/10.1007/s11464-018-0720-1
Let be an iterated function system (IFS) on with an attractor K. Let (Σ, σ) denote the one-sided full shift over the finite alphabet {1, 2, . . . , l}, and let π: Σ → K be the coding map. Given an asymptotically (sub)-additive sequence of continuous functions , we define the asymptotically additive projection pressure Pπ() and show the variational principle for Pπ() under certain affine IFS. We also obtain variational principle for the asymptotically sub-additive projection pressure if the IFS satisfies asymptotically weak separation condition (AWSC). Furthermore, when the IFS satisfies AWSC, we investigate the zero temperature limits of the asymptotically sub-additive projection pressure Pπ(β) with positive parameter β.
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On c#-normal subgroups in finite groups
Huaquan WEI, Qiao DAI, Hualian ZHANG, Yubo LV, Liying YANG
Front. Math. China. 2018, 13 (5): 1169-1178.
https://doi.org/10.1007/s11464-018-0724-x
A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G. In this paper, we investigate the influence of fewer c#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.
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Commuting variety of Witt algebra
Yu-Feng YAO, Hao CHANG
Front. Math. China. 2018, 13 (5): 1179-1187.
https://doi.org/10.1007/s11464-018-0725-9
Let g= W1 be the Witt algebra over an algebraically closed field k of characteristic p >3, and let = {(x, y) ∈g ×g | [x, y] = 0}be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250: 473–484], we show that the variety is reducible, and not equidimensional. Irreducible components of and their dimensions are precisely given. As a consequence, the variety is not normal.
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13 articles
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