Related papers: Twenty dry Martinis for the Unitary Almost Mathieu…
The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative…
Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with…
The treatment of anharmonic oscillators (including double-wells) by instanton methods is wellknown. The alternative differential equation method is not so wellknown. Here we reformulate the latter completely parallel to the strong coupling…
In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine condition or the milder Bryuno condition. In…
We study the phase transion line of the almost Mathieu operator, that separates arithmetic regions corresponding to singular continuous and a.e. pure point regimes, and prove that both purely singular continuous and a.e. pure point spectrum…
A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasi-particles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
In this paper, we investigate critical quasilinear elliptic partial differential equations on a complete Riemannian manifold with nonnegative Ricci curvature. By exploiting a new and sharp nonlinear Kato inequality and establishing some…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
We introduce and study the class of unbounded DunfordPettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.
We obtain new semiclassical estimates for pseudodifferential operators with low regular symbols. Such symbols appear naturally in a Cauchy Problem related to recent weak solutions to the unstable Muskat problem constructed via convex…
Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these…
We consider the discrete versions of the well known Borg theorem and use simple linear algebraic techniques to obtain new versions of the discrete Borg type theorems. To be precise, we prove that the periodic potential of a discrete…
Given a selfadjoint magnetic Schr\"odinger operator \begin{equation*} H = ( i \partial + A(x) )^2 + V(x) \end{equation*} on $L^{2}(\mathbb{R}^n)$, with $V(x)$ strictly subquadratic and $A(x)$ strictly sublinear, we prove that the flow…
We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the…
In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorization of this operator involving two non local operators. The…
The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the…
We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of…
This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…