| Let X be a CAT ( 1) space which is spherically symmetric around some point x0 2 X and whose boundary has nite positive s dimensional Hausdor measure. Let = ( x)x2X be a conformal density of dimension d > s=2 on @X. We prove that x0 is a weak limit of measures supported on spheres centered at x0. These measures are expressed in terms of the total mass function of and of the d dimensional spher...

Abstract_ _ We prove a common coincidence point theorem for a non-fuzzy mapping and a pair of fuzzy mappings under a ' contraction condition on a metric space in the context of Hausdor¤ metric on the family of fuzzy sets. Further, we establish a common coincidence point theorem on a metric space with the d1 metric on fuzzy sets, which extends a number of recent results. As applications, we obta...

The Weierstrass nowhere diierentiable function, and functions constructed from similar innnite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorr dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation ...

There is mounting evidence Man77, Sch91] that real datasets are statistically self-similar, and thus, `fractal'. This is an important insight since it permits a compact statistical description of spatial datasets; subsequently, as we show, it also forms the basis for the theoretical analysis of spatial access methods, without using the typical, but unrealistic, uniformity assumption. In this pa...

We investigate the complexity of sets that have a rich internal structure and at the same time are reducible to sets of either low or very high information content. In particular, we show that every length-decreasing or word-decreasing self-reducible set that reduces to some sparse set via a non-monotone variant of the Hausdorr reducibility is low for p 2. Measuring the information content of a...

1. Uni ed eld theories suggest a N dimensional conguration space with N̄ = N−4 > 0 extra dimensions not perceived in nature. The common heuristic reasons for this proposition are: (i) the volume [Hausdor measure] does not scale like μH(δ,R ) = δ μH(1,R ), where δ is some length scale and 1 stands for its unity. Instead, experience tells us that increasing (or decreasing) the spacial size of an o...

let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

Few studies have examined the impact of age on reactivity to concurrent think-aloud (TA) verbal reports. An initial study with 30 younger and 31 older adults revealed that thinking aloud improves older adult performance on a short form of the Raven's Matrices (Bors & Stokes, 1998, Educational and Psychological Measurement, 58, p. 382) but did not affect other tasks. In the replication experimen...

Abstract: Comparing probability or possibility distributions is important in many elds of information processing under uncertainty. In this paper we address the question of de ning and computing Hausdor distances between distributions in a general sense. We propose several dilations of distributions, and exhibit some links betweenLévy-Prokhorovdistances anddilation-baseddistances. In particular...