相关论文: Repetitions in beta-integers

In this paper we show how quantum corrections, although perturbatively small, may play an important role in the analysis of the existence of some classical models. This, in fact, appears to be the case of static, uniform--density models of…

An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…

We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. So the…

In this paper we deal with a classical problem in elementary number theory, namely repeating decimals. We show how the digits of the period of the decimal representation of any fraction $\frac{k}{m}$, where $k$ and $m$ are positive integers…

In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…

We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…

A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of…

This paper uses 3D grain-scale finite element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal…

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an…

The volume coherent deflection of high-energy positive and negative particles in uniformly bent crystals is studied. The general analysis of potential scattering shows that the standard screening potential for a large class of collisions…

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…

The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the…

Within the replica framework we study analytically the instance space of the number partitioning problem. This classic integer programming problem consists of partitioning a sequence of N positive real numbers $\{a_1, a_2,..., a_N}$ (the…

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…

We establish the existence of `time quasicrystals', tilings of the time axis with two unit cells of different duration. These aperiodic tilings can be constructed as slices through regular tilings of a space spanned by two orthogonal time…

What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…

In this paper, we prove results on enumerations of sets of Rota-Baxter words in a finite number of generators and a finite number of unary operators. Rota-Baxter words are words formed by concatenating generators and images of words under…

Classically in combinatorics on words one studies unavoidable regularities that appear in sufficiently long strings of symbols over a fixed size alphabet. In this paper we take another viewpoint and focus on combinatorial properties of long…

The problem of computing the cardinality of the intersection of multiple balls in the Hamming space has attracted a lot of attention recently due to their applications in the list reconstruction problem and information retrieval in…