Related papers: Transient Reviving Dynamics with an Exact Solution…
We investigate how the theory of self-adjoint differential equations alone can be used to provide a satisfactory solution of the inverse vatiational problem. For the discrete system, the self-adjoint form of the Newtonian equation allows…
This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…
We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schr\"odinger equation is written through the first derivative of a double-confluent Heun function. One of…
The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\lambda \phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
Measuring attenuation coefficients is a fundamental problem that can be solved with diverse techniques such as X-ray or optical tomography and lidar. We propose a novel approach based on the observation of a sample from a few different…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
We study transient behaviour in the dynamics of complex systems described by a set of non-linear ODE's. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The…
This study presents an analytical method for tuning PI controllers in First-Order with Time Delay (FOTD) systems, leveraging the Lambert W function. The Lambert W function enables exact pole placement, yielding analytical expressions for PI…
We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
In the present work, the results obtained in [1] about the revivals of a relativistic fermion wave function on a torus are considerably enlarged. In fact, all the possible quantum states exhibiting revivals are fully characterized. The…
Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable $X$ into a so-called Lambert $W$ random variable $Y$,…
We introduce the parafermionic truncated Wigner approximation ($p$TWA), a semiclassical phase-space framework for simulating the nonequilibrium dynamics of lattice systems with fractional exchange statistics. The method extends truncated…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex…