We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bas...

We address the dynamics of cellular automaton (CA) that multiplies by p/q in base pq (for coprime p>q>1) studying its trace subshift. present a conjugacy to previously studied base-p/q numeration system. also show subshift is not synchronizing and particular sofic. As byproduct we compute complexity function conclude presenting an example sofic shift with same function.

1.1. Gaussian random fields on manifolds. Let X(p), p ∈ M̃ , be a realvalued random field on an orientable manifold M̃ . In this article, we consider a Gaussian random field with a smooth sample path and one-dimensional standard normal marginals (i.e., X(p) ∼ N(0, 1) for each p ∈ M̃). Let r(p, q) = Cov(X(p), X(q)) denote the covariance function. If r(p, q) is sufficiently smooth in a neighborhood ...

For shallow caps under an axisymmetric external pressure distribution which is inward (with a representative magnitude pO) in a neighborhood of the pole and outward away from the pole, it has been shown previously that a finite axisymmetric dimple state of deformation is possible if p0 is at least of the order of the classical buckling pressure for a complete spherical shell, Pi, and that, asym...

Studies show that residents of disadvantaged neighborhoods drink more heavily than residents of more affluent neighborhoods. However, explanations for this association are not well developed. Using data collected from a sample of low-income women with children from Boston, Chicago, and San Antonio, we explore the possibility that perceptions of neighborhood disorder encourage heavy drinking. Dr...

Here the canonical contact structure ξ0 on a lens space L(p, q) is the descendant of the distribution of complex lines on S = {(z1, z2) | |z1| + |z2| = 1} under the quotient map S → L(p, q) of the Zp-action (z1, z2) 7→ (μpz1, μpz2). (Here μp = exp( √ −1 p ), and p, q are relatively prime and 0 < q < p.) The contact structure ξ0 induces a canonical orientation on L(p, q) where a volume form is g...

Abstract Suppose that we are given a contact sub-Riemannian manifold ( M , H g ) of dimension 3 such the Reeb vector field is an infinitesimal isometry (such manifolds will be referred to as special). For point $$q\in M$$ q ∈ M denote by $$\mathfrak {i}...

A first example of a connection between transcendental numbers and complex dynamics is the following. Let p and q be polynomials with complex coefficients of the same degree. A classical result of Böttcher states that p and q are locally conjugates in a neighborhood of∞: there exists a function f , conformal in a neighborhood of infinity, such that f(p(z)) = q(f(z)). Under suitable assumptions,...

The discrete logarithm over finite fields of small characteristic can be solved much more efficiently than previously thought. This algorithmic breakthrough is based on pinpointing relations among the factor base discrete logarithms. In this paper, we concentrate on the Kummer extension Fq2(q−1) = Fq2 [x]/(x q−1 − A). It has been suggested that in this case, a small number of degenerate relatio...

The neighborhood has been used as a sampling unit for exploring variations in health outcomes. In a variety of studies census tracts or ZIP codes have been used as proxies for neighborhoods because the boundaries are pre-defined units for which other data are readily available. However these spatial units can be arbitrary and do not account for social-cultural behaviors and identities that are ...