Related papers: What is Aperiodic Order?

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…

Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a…

An interval $k$-graph is the intersection graph of a family $\mathcal{I}$ of intervals of the real line partitioned into at most $k$ classes with vertices adjacent if and only if their corresponding intervals intersect and belong to…

We present a theory of lazy imperative timing.

In this text we are going to discuss the relation between monodromy and algebraic cycles.

An introduction to Hyperbolic Analysis is presented.

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

The microscopic description of spin-Peierls substances is discussed. Particular attention is paid to the ordered (dimerised and incommensurably modulated) phases. Important points are the adiabatic and the antiadiabatic approach, generic…

The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having…

We examine how time ordering works in quantum mechanics and in classical mechanics.

This article is about discrete periodicities and their combinatorial structure. It describes the unique structure caused by the alteration of a pattern in a repetition. That alteration of a pattern could be "heard" as the disturbance that…

In this paper we give an ordinal analysis of a set theory with $\Pi_{1}$-Collection.

We formulate and discuss a general axiomatic theory of arbitrary objects. This theory is expressed in a simple first-order language without modal operators, and it is governed by classical logic.

The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…

In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no…

This is a survey on the recent theory of chaos in partial differential equations.

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…

We prove the irrationality of some factorial series. To do so we combine methods from elementary and analytic number theory with methods from the theory of uniform distribution.

We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a…

Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Raindrops in A minor. We also discuss connections between…