Related papers: Substitution Delone Sets

Given a family $\mathcal{F}=\{A_1,\dots,A_s\}$ of subsets of $\mathbb{Z}_n$, define $\Delta \mathcal{F}$ to be the multiset of all (cyclic) distances dist$(x,y)$, where $\{x,y\} \subset A_i$, $x \neq y$, for some $i=1,\dots,s$. Taking…

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…

The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…

Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several…

This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and can be understood as that of giving…

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal…

Algebraic holonomic $\mathcal{D}$-modules on a complex line are classified by the associated topological data consisting of local systems with Stokes structure and the nearby and vanishing cycles at the singularities. The Fourier transform…

In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…

This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of…

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…

We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…

This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…

Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…

When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…

Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear…

We extend a discrepancy bound of Lagarias and Pleasants for local weight distributions on linearly repetitive Delone sets and show that a similar bound holds also for the more general case of Delone sets without finite local complexity if…

We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions…

This article describes a structure that metric spaces can be equipped with so that they resemble normed vector spaces and examines necessary and sufficient conditions for the existence of such a structure on a general metric space.

In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous at x. We give conditions under which the latter set is…