Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace–Beltrami operator

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

Single-transistor Chaotic Oscillators with Preassigned Spectrum

In this report the problem of forming chaotic signals with prescribed spectrum is discussed. An approach to construction of single-transistor chaotic oscillators with preassigned spectrum on the basis of “active component (transistor) – passive quadripole closed in feedback loop” structure is proposed. On example of capacitive three-point oscillator it is shown that in the oscillator with such ...

Two Remarks on the Length Spectrum of a Riemannian Manifold

We demonstrate that every closed manifold of dimension at least two admits smooth metrics with respect to which the length spectrum is not a discrete subset of the real line. In contrast, we show that the length spectrum of any real analytic metric on a closed manifold is a discrete subset of the real line. In particular, the length spectrum of any closed locally homogeneous space forms a discr...

The Gaps in the Spectrum of the Schrödinger Operator

Schrödinger Operator on Homogeneous Metric Trees : Spectrum in Gaps

The paper studies the spectral properties of the Schrödinger operator A gV = A 0 + gV on a homogeneous rooted metric tree, with a decaying real-valued potential V and a coupling constant g ≥ 0. The spectrum of the free Laplacian A 0 = −∆ has a band-gap structure with a single eigenvalue of infinite multiplicity in the middle of each finite gap. The perturbation gV gives rise to extra eigenvalue...