A two-dimensional visual device for description of the dispersion of a multivariate data set in any dimension is the scale curve, a depth-based method introduced by Liu (1990) and treated in detail by Liu, Parelius and Singh (1999). It offers an appealing alternative to covariance matrix methods and even provides an attractive new tool in the univariate case. To support applications such as uni...

Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...

We prove a simple uniform continuity bound for the sandwiched Rényi conditional entropy α ∈ [1/2, 1) ∪ (1, ∞], which is independent of dimension conditioning system.

A new method for estimating fractal dimension of tree crowns from digital images is presented. Three species of trees, Japanese yew (Taxus cuspidata Sieb & Zucc), Hicks yew (Taxus × media), and eastern white pine (Pinus strobus L.), were studied. Fractal dimensions of Japanese yew and Hicks yew range from 2.26 to 2.70. Fractal dimension of eastern white pine range from 2.14 to 2.43. The differe...

In various technological and scientific applications, different types of coil systems are being used to produce uniform alternating magnetic field. The dimensions of these coil systems are considerably larger than the volume of interest. There is a necessity to reduce the dimension of the coil system without sacrificing the extent of uniformity of the magnetic field. This problem has a wide aud...

In this paper we study diffusion schemes for dynamic load balancing on message passing multiprocessor networks. One of the main results concerns conditions under which these dynamic schemes converge and their rates of convergence for arbitrary topologies. These results use the eigenstructure of the iteration matrices that arise in dynamic load balancing. We completely analyze the hypercube netw...