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51.
For one-dimensional expanding mapsT with an invariant measure we consider, in a parameter space, the envelope
n
of the real lines associated to any couple of points of the orbit, connected byn iterations ofT. If the map hass inverses and is piecewise linear, then the sets
n
are just the union ofs
n
points and converge to the invariant Cantor set ofT. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on 1 to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and hass inverses, the sets
n
are homeomorphic to the Cantor set; they converge to the Cantor set ofT and their measures converge to the measure of the Cantor set whenn. The correspondence between the sets
n
allows one to define converging approximation schemes for the map an its measure: one replaces each of thes
n
disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set 1. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined. 相似文献
52.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
53.
Validity and Reliability of the Reflux Symptom Index (RSI) 总被引:14,自引:0,他引:14
Laryngopharyngeal reflux (LPR) is present in up to 50% of patients with voice disorders. Currently, there is no validated instrument that documents symptom severity in LPR. We developed the reflux symptom index (RSI), a self-administered nine-item outcomes instrument for LPR. The purpose of this investigation was to evaluate the psychometric properties of the RSI. For validity assessment, 25 patients with LPR were evaluated prospectively before and six months after b.i.d. treatment with proton pump inhibitors (PPI). Each patient completed the RSI as well as the 30-item voice handicap index (VHI). For reliability assessment, the study patients were given the RSI on two separate occasions before the initiation of treatment. Normative RSI data were derived from 25 age-matched and gender-matched controls taken from an existing database of asymptomatic individuals without any evidence of LPR. The mean RSI (+/- standard deviation) of patients with LPR improved from 21.2 (+/- 10.7) to 12.8 (+/- 10.0), and the mean VHI improved from 52.2 (+/- 24.7) to 41.5 (+/- 25.0) after 6 months of therapy (p = 0.001 and 0.065, respectively). Of the three VHI subscales (emotional, physical, functional), only the functional subscale improved significantly (p = 0.037). Patients who experienced a five point or better improvement in RSI were 11 times more likely to experience a five-point improvement in VHI (95% confidence interval = 1.7, 76.8). For reliability assessment, the first and second pretreatment RSIs were 19.9 (+/- 11.1) and 20.9 (+/- 9.6), respectively (correlation coefficient = 0.81, p < 0.001). The single-item correlation coefficients ranged from 0.41 to 0.91 (p < 0.05 for all items). The mean pretreatment RSI in patients with LPR was significantly higher than controls (21.2 versus 11.6; p < 0.001). The mean RSI of patients with LPR after 6 months of PPI therapy approached that of asymptomatic controls (p > 0.05). The RSI is easily administered, highly reproducible, and exhibits excellent construct and criterion-based validity. 相似文献
54.
本文引进了H-值半鞅测度,研究了其基本性质和与之相联系的随机积分,本文还引入了H-值半鞅测度序列依分布弱收敛的概念,建立了H-值半鞅测度的极限定理,给出了H-值半鞅测度弱收敛的条件。 相似文献
55.
What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004 相似文献
56.
Carlo Bertoluzza Pedro Miranda Pedro Gil 《International Journal of Approximate Reasoning》2005,40(3):127-146
In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures. 相似文献
57.
Fu Xianlong Zhou Lei Cao Yueju 《Annals of Differential Equations》2005,21(3):275-278
In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method. 相似文献
58.
总结Riemann积分的发展历史、基本思想及其各种推广,介绍Riemann积分的局限性和缺陷,以及由此推动产生Lebesgue积分的过程. 相似文献
59.
为减小油气输送难度和避免原油固化,石油、天然气通常在高温高压下输送.输送过程中的高温和高压导致海底管线中产生较大的附加应力,附加应力的不断累积造成管线发生整体屈曲.对于埋地的海底管线通常会产生竖向屈曲大变形而影响使用甚至破坏.因此,需对有可能产生整体屈曲的管线采取工程防护措施.结合我国海洋工程中管线常用的铺设及保护措施,对处于保护状态下管线由温度应力引起的整体屈曲特性进行理论分析和数值推导,对沟槽保护、沟槽掩埋保护以及压块保护措施的有效性进行了系统分析和对比. 相似文献
60.