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For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model…
We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional…
This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…
Asymptotic dynamics of ordinary differential equations (ODEs) are commonly understood by looking at eigenvalues of a matrix, and transient dynamics can be bounded above and below by considering the corresponding pseudospectra. While…
In computing the third order terms of the series of powers of the center manifold at an equilibrium point of a scalar delay differential equation, with a single constant delay $r>0,$ some problems occur at the term $w_{21}z^2\bar{z}.$ More…
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…
There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter…
A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than…
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function…
We consider the energy-critical non-linear focusing wave equation in dimension N=3,4,5. An explicit stationnary solution, $W$, of this equation is known. The energy E(W,0) has been shown by C. Kenig and F. Merle to be a threshold for the…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
In a recent article, we introduced and studied a precise class of dynamical systems called solvable systems. These systems present a dynamic ruled by discontinuous ordinary differential equations with solvable right-hand terms and unique…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
We compare the classical viscoelastic models due to Becker and Lomnitz with respect to a recent viscoelastic model based on the Lambert W function. We take advantage of this comparison to derive new analytical expressions for the relaxation…
We address an inverse problem in non-Archimedean dynamics: given a finite discrete dynamical system (equivalently, a functional graph on $N$ states), construct a continuous $p$-adic dynamical system whose residue-level behavior reproduces…
We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive…