Related papers: Linearization of the box-ball system: an elementar…
The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the…
The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
We construct a stochastic particle system which is a multi-species version of the q-Boson system due to Sasamoto and Wadati. Its transition rate matrix is obtained from a representation of a deformation of the affine Hecke algebra of type…
Analytical tools to $K$-theory; namely, self-stabilization of rapidly decreasing matrices, linearization of cyclic loops, and the contractibility of the pointed stable Toeplitz algebra are discussed in terms of concrete formulas. Adaptation…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
Description of time evolution of the relativistic unstable electromagnetic system consisting of Fermi-Dirac particle interacting with electromagnetic field, in the framework of the Liouville space extension of quantum mechanics is done. The…
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…
The box-ball system (BBS) is a cellular automaton that is an ultradiscrete analogue of the Korteweg--de Vries equation, a non-linear PDE used to model water waves. In 2001, Hikami and Inoue generalised the BBS to the general linear Lie…
Lattice formulations of QCD with Wilson fermions and a chirally twisted quark mass matrix provide an attractive framework for non-perturbative numerical studies. Owing to reparameterization invariance, the limiting continuum theory is just…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
This work focuses on modeling of time-varying covariance matrices using the state covariance of linear stochastic systems. Following concepts from optimal mass transport and the Schr\"odinger bridge problem (SBP), we investigate several…
We construct the causal fermion system for globally hyperbolic spacetimes starting in the framework of algebraic quantum field theory. The fermionic projector is identified with the one-particle density operator of a quasi-free Hadamard…
A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas…
Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and…
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…