Annular functions form a residual set.

1975 ◽  
Vol 1975 (272) ◽  
pp. 23-24
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.


1984 ◽  
Vol 96 (3) ◽  
pp. 413-423 ◽  
Author(s):  
Claude Tricot

AbstractLet (Dn) be the apollonian packing of a curvilinear triangle T, ρn the radius of Dn, E = T—U Dn the residual set, dim (E) its Hausdorff dimension. In this paper we give a new proof of the equality dim proved by Boyd [2]. Our technique is to construct a sequence of regular triangles covering E, and suitable measures μkcarried by E which allow us to apply a density theorem.


2011 ◽  
Vol 26 (1) ◽  
pp. 283-297 ◽  
Author(s):  
Luis Bernal-González ◽  
Antonio Bonilla

Author(s):  
Jun Zhan ◽  
Ronglin Wang ◽  
Lingzhi Yi ◽  
Yaguo Wang ◽  
Zhengjuan Xie

The output power of wind turbine has great relation with its health state, and the health status assessment for wind turbines influences operational maintenance and economic benefit of wind farm. Aiming at the current problem that the health status for the whole machine in wind farm is hard to get accurately, in this paper, we propose a health status assessment method in order to assess and predict the health status of the whole wind turbine, which is based on the power prediction and Mahalanobis distance (MD). Firstly, on the basis of Bates theory, the scientific analysis for historical data from SCADA system in wind farm explains the relation between wind power and running states of wind turbines. Secondly, the active power prediction model is utilized to obtain the power forecasting value under the health status of wind turbines. And the difference between the forecasting value and actual value constructs the standard residual set which is seen as the benchmark of health status assessment for wind turbines. In the process of assessment, the test set residual is gained by network model. The MD is calculated by the test residual set and normal residual set and then normalized as the health status assessment value of wind turbines. This method innovatively constructs evaluation index which can reflect the electricity generating performance of wind turbines rapidly and precisely. So it effectively avoids the defect that the existing methods are generally and easily influenced by subjective consciousness. Finally, SCADA system data in one wind farm of Fujian province has been used to verify this method. The results indicate that this new method can make effective assessment for the health status variation trend of wind turbines and provide new means for fault warning of wind turbines.


1970 ◽  
Vol 13 (1) ◽  
pp. 59-64 ◽  
Author(s):  
David W. Boyd

If U is an open set in Euclidean N-space EN which has finite Lebesgue measure |U| then a complete packing of U by open spheres is a collection C={Sn} of pairwise disjoint open spheres contained in U and such that Σ∞n=1|Sn| = |U|. Such packings exist by Vitali's theorem. An osculatory packing is one in which the spheres Sn are chosen recursively so that from a certain point on Sn+1 is the largest possible sphere contained in (Here S- will denote the closure of a set S). We give here a simple proof of the "well-known" fact that an osculatory packing is a complete packing. Our method of proof shows also that for osculatory packings, the Hausdorff dimension of the residual set is dominated by the exponent of convergence of the radii of the Sn.


1975 ◽  
Vol 56 ◽  
pp. 163-170
Author(s):  
Akio Osada

The purpose of this paper is to study the distribution of Fatou points of annular functions introduced by Bagemihl and Erdös [1]. Recall that a function f(z), regular in the open unit disk D: | z | < 1, is referred to as an annular function if there exists a sequence {Jn} of closed Jordan curves, converging out to the unit circle C: | z | = 1, such that the minimum modulus of f(z) on Jn increases to infinity. If the Jn can be taken as circles concentric with C, f(z) will be called strongly annular.


2008 ◽  
Vol 28 (4) ◽  
pp. 1291-1322 ◽  
Author(s):  
RONNIE PAVLOV

AbstractIn this paper, we exhibit, for any sparse-enough increasing sequence {pn} of integers, totally minimal, totally uniquely ergodic, and topologically mixing systems (X,T) and (X′,T′) and f∈C(X) for which the averages $({1}/{N}) \sum _{n=0}^{N-1} f(T^{p_n} x)$ fail to converge on a residual set in X, and where there exists x′∈X′ with $x' \notin \overline {\{T'^{p_n} x'\}}$.


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