scholarly journals Universal factorizations of quasiperiodic functions

2015 ◽  
Author(s):  
Michael Robinson
Keyword(s):  
Quasiperiodic Functions

Description and symmetry of aperiodic crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Time Reversal ◽  
Mathematical Concept ◽  
New Materials ◽  
Magnetic Systems ◽  
Atomic Structures ◽  
Modulated Phases ◽  
Quasiperiodic Functions ◽  
Aperiodic Crystals ◽  
Superspace Description

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

Vortex structure and characterization of quasiperiodic functions

2002 ◽  
Vol 35 (47) ◽  
pp. 10101-10116 ◽  
Author(s):  
Itzhack Dana ◽  
Vladislav E Chernov
Keyword(s):  
Vortex Structure ◽  
Quasiperiodic Functions

scholarly journals On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
A. Lastra ◽  
S. Malek
Keyword(s):  
Perturbation Parameter ◽  
Formal Series ◽  
Cauchy Problems ◽  
Small Divisor ◽  
Real Numbers ◽  
Positive Real ◽  
Quasiperiodic Function ◽  
Quasiperiodic Functions ◽  
The Difference ◽  
Formal Power

We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin.

scholarly journals Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Shanliang Zhu ◽  
Shufang Zhang ◽  
Xinli Zhang ◽  
Qingling Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Singularly Perturbed ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Quasiperiodic Solutions ◽  
Quasiperiodic Functions ◽  
Fixed Point Methods

In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.

Properties of quasiperiodic functions

2017 ◽  
Vol 29 (18) ◽  
pp. 184003
Author(s):  
Johannes Roth
Keyword(s):  
Quasiperiodic Functions

Exact inequalities for norms of intermediate derivatives of quasiperiodic functions

1994 ◽  
Vol 56 (6) ◽  
pp. 1300-1303 ◽  
Author(s):  
G. V. Galunov ◽  
V. L. Oleinik
Keyword(s):  
Quasiperiodic Functions ◽  
Derivatives Of
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