We study two-dimensional magnetic Schrödinger operators with a magnetic field that is equal to b > 0 for x > 0 and −b for x < 0. This magnetic Schrödinger operator exhibits a magnetic barrier at x = 0. The unperturbed system is invariant with respect to translations in the ydirection. As a result, the Schrödinger operator admits a direct integral decomposition. We analyze the band functions of ...

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

We first show asymptotic L bounds for a class of equations, which includes the Burger-Sivashinsly model for odd solutions with periodic boundary conditions. We consider the conditional stability of stationary solutions of Kuramoto-Sivashinsky equation in the periodic setting. We establish rigorously the general structure of the spectrum of the linearized operator. In addition, we show condition...

In a recent study we have obtained correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N × N matrices, both in the bulk and at the soft edge of the spectrum. In the present study these results are used to similarly analyze the eigenvalue density for Gaussian and Laguerre random matrix ensembles with or...

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form H = dΓ(ω) + V acting on the bosonic Fock space Γ(h), where ω is a massive one-particle Hamiltonian acting on h and V is a Wick polynomial Wick(w) for a kernel w satisfying some decay properties at infinity. We describe the essential spectrum of H , prov...

This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic regime, the fundamental limits of fixed-to-variable lossless compression with and without prefix constraints are shown to be tightly coupled. Several precise, quantitative bounds are derived, connecting the distr...

For geometrically nite Kleinian groups with parabolic elements we study that part of the Lagrange spectrum which does not lie in the Markov spectrum. Using the ergodicity of the associated geodesic ow with respect to the Liouville{Patterson measure, we obtain an estimate for the asymptotic frequency with which recurrent geodesics enter certain cusp regions. In particular, this allows a quantita...

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

In this study, the authors consider the asymptotic capacity of wireless multicast and unicast transmission schemes in a spectrum-sharing system. In these schemes, a secondary access point (SAP) utilises the licensed spectrum of an active primary user (PU) to send a common information to multiple secondary users simultaneously, as long as the interference power inflicted on the PU is less than a...

We consider semiparametric log periodogram regression estimation of memory parameter for the latent process in long memory stochastic volatility models. It is known that though widely used among researchers, the Geweke and Porter-Hudak (1983; GPH) LP estimator violates the Gaussian or Martingale assumption, which results in significant negative bias due to the existence of the spectrum of non-G...