Modeling UpLink power control with outage probabilities
Kenneth L. Clarkson, K. Georg Hampel, et al.
VTC Spring 2007
We study finitely generated, abelian groups Γ of continuous automorphisms of a compact, metrizable group X and introduce the descending chain condition for such pairs (X, Γ). If Γ acts expansively on X then (X, Γ) satisfies the descending chain condition, and (X, Γ) satisfies the descending chain condition if and only if it is algebraically and topologically isomorphic to a closed, shift-invariant subgroup of GΓ, where G is a compact Lie group. Furthermore every such subgroup of GΓ is a (higher dimensional) Markov shift whose alphabet is a compact Lie group. By using the descending chain condition we prove, for example, that the set of Γ-periodic points is dense in X whenever Γ acts expansively on X. Furthermore, if X is a compact group and (X, Γ) satisfies the descending chain condition, then every ergodic element of Γ has a dense set of periodic points. Finally we give an algebraic description of pairs (X, Γ) satisfying the descending chain condition under the assumption that X is abelian. © 1989, Cambridge University Press. All rights reserved.
Kenneth L. Clarkson, K. Georg Hampel, et al.
VTC Spring 2007
W.C. Tang, H. Rosen, et al.
SPIE Optics, Electro-Optics, and Laser Applications in Science and Engineering 1991
Shashanka Ubaru, Lior Horesh, et al.
Journal of Biomedical Informatics
R.A. Brualdi, A.J. Hoffman
Linear Algebra and Its Applications