In this paper we present a new method for proving the existence of an eigenvalue below the essential spectrum for Sturm-Liouville operators with coefficients which are L1 perturbations of periodic functions. This method combines operator theory and “standard” numerical analysis with interval arithmetic analysis. We illustrate the method by showing that the SturmLiouville problem (SLP) consistin...

The existence and stability of travelling waves are typically investigated on unbounded domains even though the domains in experiments or numerical simulations are bounded. We are interested in the eeects that the truncation of the unbounded to a large but bounded domain has on the stability properties of a nonlinear wave. These eeects depend upon the boundary conditions that are imposed on the...

Autism spectrum disorder (ASD) is highly genetic in its etiology, with potentially hundreds of genes contributing to risk. Despite this heterogeneity, these disparate genetic lesions may result in the disruption of a limited number of key cell types or circuits-information which could be leveraged for the design of therapeutic interventions. While hypotheses for cellular disruptions can be iden...

The essential spectrum of multiparticle Brown– Ravenhall operators is characterized in terms of two–cluster decompositions for a wide class of external fields and interparticle interactions and for the systems with prescribed symmetries. 2000 Mathematics Subject Classification: 81V55, 81Q10

Essential hypertension is thought to produce a uniform exaggerated natriuresis and diuresis. Because validation of this formulation in humans is incomplete, the natriuretic and diuretic responses to acute volume expansion were characterized by using water immersion to the neck. This method provides a volume stimulus identical to that induced by 2 L of saline without plasma compositional change....

We establish some criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact abelian groups, in particular differential operators of any order with complex measurable coefficients on R, singular Dirac operators and Laplace-Beltrami ...

Let V be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on V contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of V , and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and m...

We show here that the spectrum of the family of noncommutative harmonic oscillators Qw(α,β)(x,D) for α, β ∈ R+ in the range αβ = 1, is [0,+∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Qw(α,β)(x,D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extends the...

In this short paper, the usage of truncation method to get information about essential spectrum of bounded as well as semi-bounded linear operators on separable Hilbert spaces, is investigated. In addition to this, the problem of predicting the gaps in the essential spectrum of self-adjoint operators, linear algebraically is also considered.

The bifurcation of internal modes from the phonon band in models supporting solitary wave solutions has been one of the exciting new phenomena in the field. We will present a number of analytical and semi-analytical techniques for the detection, study and understanding of these modes. We will see how they appear, without threshold, due to the discretization of the continuum equations. This pert...