Dubuc’s interpolatory four-point scheme inserts a new point by fitting a cubic polynomial to neighbouring points over uniformly spaced parameter values. In this paper we replace uniform parameter values by chordal and centripetal ones. Since we update the parameterization at each refinement level, both schemes are non-linear. Because of this data-dependent parameterization, the schemes are only...

This paper presents a generalization of Catmull-Clark-variant Doo-Sabin surfaces and non-uniform biquadratic B-spline surfaces called NURDSes (Non-Uniform Recursive Doo-Sabin Surfaces). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo-Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergen...

We study the Abelian sandpile model on Z. In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ, and study ergodic properties of this process. The main techniques we use are a connection between the st...

We study the Abelian sandpile model on Z. In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ, and study ergodic properties of this process. The main techniques we use are a connection between the st...

The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed-point equations. Covariances, asymptotic correlations, and bivariate ...

A solution to the BI action describing an expanded D3-brane is considered. The configuration is not supersymmetric but is supported against collapse by the Poynting vector. In the uniform magnetic field limit, the brane magnetic charge grows without limit while the energy and the radius of the brane remain finite. In this limit the brane consists of a large number of small D-strings forming a h...

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size n → ∞. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results hold uniformly over the bandwidth h, restricted to vary in [h n , h n ], where {h n } n≥1 and {h ′′ n } n≥1 are appropriate nonrandom sequences. We treat the case wh...

The complexity of the algorithm Radix Selection is considered for independent data generated from a Markov source. The complexity is measured by the number of bucket operations required and studied as a stochastic process indexed by the ranks; also the case of a uniformly chosen rank is considered. The orders of mean and variance of the complexity and limit theorems are derived. We find weak co...

For turbulent boundary-layer flow under a uniform freestream speed U∞ over a plate of length L, covered with uniform roughness of nominal sand-grain scale ks , the physical behaviors underlying two distinguished limits at large ReL ≡ U∞L/ν are explored: the fully rough wall flow where ks/L is fixed and the long-plate limit where Rek ≡ U∞ks/ν is fixed. For the fully rough limit it is shown that ...