Related papers: Analytical Periodic Solutions of Weakly Coupled Ma…
Analytic versions of QCD are those whose coupling alpha_s(Q^2) does not have the unphysical Landau singularities on the space-like axis (-q^2=Q^2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q^2 <…
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton--Jacobi equations can be approximated by iterated twisted Lax--Oleinik like operators. We establish convergence to the solution of the iterated scheme and…
In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
Several theorems are demonstrated that determine the sufficient conditions for the existence of synchronized states (periodical and chaotic) and also of travelling waves in a CML. Also are analytically proven the existence of…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
Symmetry sharing facilitates coherent interfaces which can transition from periodic to aperiodic structures. Motivated by the design and construction of such systems, we present hexagonal aperiodic tilings with a single edge-length which…
In this paper, we first introduce the new class of vertically-recurrent matrices, using a generalization of "the Hockey stick and Puck theorem" in Pascal's triangle. Then, we give an interesting formula for the lower triangular…
We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
By a classical result, solutions of analytic elliptic PDEs, like the Laplace equation, are analytic. In many instances, the properties that come from being analytic are more important than analyticity itself. Many important equations are…
The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results…
We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices,…
Analytic smooth solutions of a general, strongly parabolic semi-linear Cauchy problem of $2m$-th order in $\mathbb{R}^N\times (0,T)$ with analytic coefficients (in space and time variables) and analytic initial data (in space variables) are…