Related papers: Model sets, almost periodic patterns, uniform dens…

Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of…

A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of…

We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this…

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…

We study discrete Laplacians on two-dimensional lattices under modular iterations, focusing on the emergence of nontrivial large-scale patterns. While purely binary or constant modular sequences quickly collapse into strict periodicity, the…

Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize…

For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither zero nor one. We quantify this statement, following work by V. Kolyada, and obtain the…

A discrete set $A$ in the Euclidian space is almost periodic if the measure with the unite masses at points of the set is almost periodic in the weak sense. We investigate properties of such sets in the case when $A-A$ is discrete. In…

Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…

We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…

We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…

A continuous-time dynamical system with parameter $\varepsilon$ is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as $\varepsilon$ approaches 0. Nearly-periodic maps are discrete-time analogues…

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass…

We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…

We study random perturbations of quasi-periodic uniformly discrete sets in the $d$-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set $X$ can be almost surely recovered from its…

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…