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991.
Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps. 相似文献
992.
Sergi Elizalde 《Journal of Combinatorial Theory, Series A》2011,118(8):2474-2497
Given a real number β>1, a permutation π of length n is realized by the β-shift if there is some x∈[0,1] such that the relative order of the sequence x,f(x),…,fn−1(x), where f(x) is the fractional part of βx, is the same as that of the entries of π. Widely studied from such diverse fields as number theory and automata theory, β-shifts are prototypical examples of one-dimensional chaotic dynamical systems. When β is an integer, permutations realized by shifts were studied in Elizalde (2009) [5]. In this paper we generalize some of the results to arbitrary β-shifts. We describe a method to compute, for any given permutation π, the smallest β such that π is realized by the β-shift. We also give a way to determine the length of the shortest forbidden (i.e., not realized) pattern of an arbitrary β-shift. 相似文献
993.
That there is a close connection between crude (or suspended) Hopf invariants and the reduced diagonal map has long been known. In this paper we build on a classical result of Boardman and Steer (1967) to explore some further relationships in terms of conic structures. In a related result we show that certain Toda brackets contain crude Hopf invariants as elements. In particular, using this latter observation, detection of crude Hopf invariants can be carried out. 相似文献
994.
Qunying LIAO 《数学年刊B辑(英文版)》2011,32(1):89-98
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. The main problem
is to compute the error distance of a received word. Using the Weil bound for character sum estimate, Li and Wan showed that
the error distance can be determined when the degree of the received word as a polynomial is small. In the first part, the
result of Li and Wan is improved. On the other hand, one of the important parameters of an error-correcting code is the dimension.
In most cases, one can only get bounds for the dimension. In the second part, a formula for the dimension of the generalized
trace Reed-Solomon codes in some cases is obtained. 相似文献
995.
The authors study the finite decomposition complexity of metric spaces of H, equipped with different metrics, where H is a subgroup of the linear group GL∞(ℤ). It is proved that there is an injective Lipschitz map φ: (F, d
S
) → (H, d), where F is the Thompson’s group, dS the word-metric of F with respect to the finite generating set S and d a metric of H. But it is not a proper map. Meanwhile, it is proved that φ: (F, d
S
) → (H, d
1) is not a Lipschitz map, where d
1 is another metric of H. 相似文献
996.
997.
本文主要研究了三角代数上的初等映射的可加性.利用矩阵分块理论,证明了三角代数上的初等映射是可加的. 相似文献
998.
为了实现在连续性空间中的离散分段问题,采用解决离散性问题的方法虚拟构造连续性集合,将连续性问题映射为分段的离散问题,根据集合中元素的离散特性实现连续性模型的分段求解.通过数据结构的设计与压缩路径的算法证实,模型的映射能够解决实际问题的分段求解. 相似文献
999.
In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasisymmetric mapping is not always harmonic. 相似文献
1000.
Inspired by the construction of blow-up solutions of the heat flow of harmonic maps from D^2 into S^2 via maximum principle (Chang et al., J. Diff. Geom., 36, 1992, pp. 507-515.) we provide examples of nonexistence of smooth axially symmetric harmonic maps from B^3 into S^2 with smooth boundary maps of degree zero. 相似文献