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By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
We examine the moments of the number of lattice points in a fixed ball of volume V for lattices in Euclidean space which are modules over the ring of integers of a number field K. In particular, denoting by ωK the number of roots of unity in K, we ...
By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...
Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...
In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...
A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer k and every δ>0 there exists n such that every subset of ${1, ...
This paper considers vessel scheduling with pilotage and tugging constraints in berthing operations with channel restrictions at seaports. To our knowledge, pilotage and tugging requirements have not been simultaneously considered in the literature. This w ...
The distribution network restoration problem is by nature a mixed integer and non-linear optimization problem due to the switching decisions and Optimal Power Flow (OPF) constraints, respectively. The link between these two parts involves logical implicati ...
An electric vehicle (EV) charging method which considers the EVs heterogeneity, taking into account the absence of any information about future arrivals and departures, and of the amount of time any charging will take. The method further considers both swi ...
